Genshin Impact: Aligning Player and Business Needs Through Data Driven Recommendations

Statement of the Research Problem

Genshin Impact has become one of the fastest growing mobile games since it came out in 2020. The popular gacha game posed the question; what drives Genshin Impact’s popularity and profitability as a leader in the gaming industry. Despite the commercial success, the continued popularity of Genshin Impact relies on keeping player satisfaction high and understanding what the player wants to better enhance the game.

The first research problem focuses on understanding the user perceptions and sentiment towards the popular video game Genshin Impact. The study aims to analyze a large dataset of tweets and specific character comments related to the game using various sentiment analysis techniques, including binary, NRC emotion, AFINN, and Jockers lexicons. By examining the sentiment expressed in these tweets, the research seeks to answer questions such as: What is the overall sentiment towards Genshin Impact among Twitter users? Are certain characters more popular? The findings of this study will provide valuable insights into user perceptions of Genshin Impact and help inform game development and community management strategies.

The second research problem focuses on exploring the top revenue-generated features of Genshin Impact characters. Part of our analysis aims to discover the crucial characteristics that contribute to the profitability of 5-star characters in “Genshin Impact” when assessing their income creation. Among the several characters available, Zhongli, Xiao, and Ganyu have proven to be the most profitable, indicating that they possess distinct qualities that strongly appeal to the player community.¹ In order to discern the distinguishing features of these characters, our research will examine their visual appeal, distinctive capabilities, and mechanics of gameplay, cross-referencing the revenue data. The purpose of this analysis is to offer developers specific information to inform future character design and game improvements.

The third research question the team answered was how to forecast revenues from banner events in Genshin Impact. The focus in this analysis was on weapons events because the events were approximately three weeks in legnth and had the structure most suited for Time Series analysis. The derived insights found that around New Years/Chinese New Year there is an uptick in revenue and pulls based on the gacha game mechanic.

#Set up the environment
library(tidyverse)

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library(skimr)
library(stringr)
library(tidytext)
library(magrittr)

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library(ggthemes)
library(wordcloud)

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library(textdata)
library(lexicon)
library(dplyr)
library(lubridate)
library(psych)

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library(rpart)
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library(mgcv)

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library(ggplot2);library(ggthemes);library(gridExtra)  # For plots

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library(quantmod);library(xts);library(zoo) # For using xts class objects

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library(forecast) # Set of forecasting functions

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library(fpp); library(fpp2) # Datasets from Forecasting text by Rob Hyndman

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library(tseries) # for a statistical test
library(dplyr) # Data wrangling
library(xts) # Creating TS Object
library(readr)

Data & Sutability

A. Text Mining - Sentiment Analysis

To understand the public reviews related to Genshin Impact, the #boycottgenshin dataset was constructed using Python by web scrapping on X (formally known as Twitter). The program is built to search Twitter for tweets containing specific hashtags on #boycottgenshin. Then, the algorithm collects various pieces of information from the tweets, including the account name of the tweet’s author, the tweet’s text, link, and different engagement metrics such as retweet count, favorite count, reply count, and quote count. The final structured dataset contains 9,883 rows with 9 columns. There are 4 character-type columns, 4 numeric-type columns, and 2 logical-type columns.

Although Genshin Impact is a relatively new game, it has a large community and a strong social media presence. The #boycottgenshin is one of the largest communities on the X platform. Therefore, the reviews from this community should reflect players’ perceptions of the game and be suitable for the analysis.

# Data Source: 
# The data comes from two sources. The first one is manually imputed 
# from paimon.moe, an in-game assistant tool. 
# The second one is from Twitter using web_scraping technique in Python. We have 
# collected all the Twitter comments using the hash tag of #boycottgenshin. 

#1: paimon.moe
#2: #boycottgenshin from Twitter, see attached python file
# Import the dataset 
genshin_reviews <- read.csv("Final_Game_Sentiment_Analysis_Data.csv")

head(genshin_reviews)

##    ACCOUNT.NAME
## 1     hxg_diluc
## 2   smearstroke
## 3    Geoff_pole
## 4      eenvvyyy
## 5 TheJackalMan7
## 6       SSJRiku
##                                                                             TWEET.LINK
## 1  https://twitter.com/hxg_diluc/status/1541312776139706368?s=20&t=1537479928677298176
## 2 https://twitter.com/smearstroke/status/1574726265331777537?s=20&t=884056268876398593
## 3  https://twitter.com/Geoff_pole/status/1569729837878607873?s=20&t=805763669061672961
## 4   https://twitter.com/eenvvyyy/status/1546793054991831040?s=20&t=1291689506228203520
## 5        https://twitter.com/TheJackalMan7/status/1571926534553997312?s=20&t=570253775
## 6    https://twitter.com/SSJRiku/status/1574405335137280002?s=20&t=1197292693610737665
##                                                                                                                                                                                                                                                                                            TWEET
## 1                                                                                                                                                                                                                                                                        No, the veil is removed
## 2                                                                     Why is this labeled as an enemy? He is just appreciating the beauty of nature. He is just mesmerized by the family of birds enjoying their afternoon sunset\n\n#boycottgenshin #fuckthisshittygame https://t.co/gsBTSxKuS7
## 3 @Luckgim @GenshinImpact You should, we all should. This game is actually a shame, very expensive, 100 euros to have only 50% of chance to get a nice character, and after that resin price, tons of items to build just character stats, sh*ty artefacts, no endgame content … #boycottgenshin
## 4    Ignore all the stupid kids. At the end of the day its just performative activism, they will go right back to playing &amp; supporting the game just like they did last year with #boycottgenshin. Na it was actually so funny how they completely forgot about Sumeru BS when fatui dropped
## 5                                                                                                                                                                                                                       @pcgamer I'll be excited after they un-whitewash Sumeru. #boycottgenshin
## 6                                      @WorldOfTeyvat #boycottgenshin and #dobettermihoyo, calling eula racist, harassment of VAs, hoyoverse bootlickers, harassment of content creators, sending death threats over ships and other meaningless things, etc. The list goes on\n\n0 stars easily
##   RETWEET.COUNTS FAVORITES REPLIES QUOTES FAVORITED RETWEETED
## 1            180      3063     167   2246     FALSE     FALSE
## 2              0         2       0      1     FALSE     FALSE
## 3              0         1       1      0     FALSE     FALSE
## 4              0         3       0      1     FALSE     FALSE
## 5              0         1       0      0     FALSE     FALSE
## 6              0         2       0      0     FALSE     FALSE

# number of rows and columns 
print(list(row = nrow(genshin_reviews), column = ncol(genshin_reviews)))

## $row
## [1] 9883
## 
## $column
## [1] 9

# check the data 
skim(genshin_reviews)

Data summary
Name	genshin_reviews
Number of rows	9883
Number of columns	9
_______________________
Column type frequency:
character	3
logical	2
numeric	4
________________________
Group variables	None

Variable type: character

skim_variable	complete_rate	min	max	n_unique
ACCOUNT.NAME	1	3	15	7985
TWEET.LINK	1	66	89	9882
TWEET	1	15	632	9780

Variable type: logical

skim_variable	n_missing	complete_rate	mean	count
FAVORITED	0	1	0	FAL: 9883
RETWEETED	0	1	0	FAL: 9883

Variable type: numeric

skim_variable	complete_rate	mean	sd	p50	p75	p100	hist
RETWEET.COUNTS	1	8.57	124.27	0	0	4584	▇▁▁▁▁
FAVORITES	1	59.87	899.19	1	4	38752	▇▁▁▁▁
REPLIES	1	2.36	33.07	0	1	1722	▇▁▁▁▁
QUOTES	1	3.18	70.38	0	0	3972	▇▁▁▁▁

# Summary of the data
summary(genshin_reviews)

##  ACCOUNT.NAME        TWEET.LINK           TWEET           RETWEET.COUNTS    
##  Length:9883        Length:9883        Length:9883        Min.   :   0.000  
##  Class :character   Class :character   Class :character   1st Qu.:   0.000  
##  Mode  :character   Mode  :character   Mode  :character   Median :   0.000  
##                                                           Mean   :   8.572  
##                                                           3rd Qu.:   0.000  
##                                                           Max.   :4584.000  
##    FAVORITES           REPLIES             QUOTES         FAVORITED      
##  Min.   :    0.00   Min.   :   0.000   Min.   :   0.000   Mode :logical  
##  1st Qu.:    0.00   1st Qu.:   0.000   1st Qu.:   0.000   FALSE:9883     
##  Median :    1.00   Median :   0.000   Median :   0.000                  
##  Mean   :   59.87   Mean   :   2.363   Mean   :   3.176                  
##  3rd Qu.:    4.00   3rd Qu.:   1.000   3rd Qu.:   0.000                  
##  Max.   :38752.00   Max.   :1722.000   Max.   :3972.000                  
##  RETWEETED      
##  Mode :logical  
##  FALSE:9883     
##                 
##                 
##                 
##

# Check distribution of numeric predictors 
genshin_reviews %>% 
  select_if(is.numeric)%>%
  pivot_longer(cols = 1:4,names_to = 'numeric_predictor', values_to = 'values')%>%
  ggplot(aes(x = values))+
  geom_histogram(binwidth = 30)+
  facet_wrap(numeric_predictor~., scales = 'free')+
  xlim(c(0, 500)) +
  ylim(c(0, 500)) +
  theme_bw()

## Warning: Removed 175 rows containing non-finite values (`stat_bin()`).

## Warning: Removed 8 rows containing missing values (`geom_bar()`).

# Check for missing values
# Show all missing data in columns
missing_data_summary <- data.frame(
  NumMissing = sapply(genshin_reviews, function(x) sum(is.na(x)))
)
print(missing_data_summary)

##                NumMissing
## ACCOUNT.NAME            0
## TWEET.LINK              0
## TWEET                   0
## RETWEET.COUNTS          0
## FAVORITES               0
## REPLIES                 0
## QUOTES                  0
## FAVORITED               0
## RETWEETED               0

# Analysis on the reviews
## Sample Review, review 3000
genshin_reviews$TWEET[3000]

## [1] "Omg, I wishGenshin will stay alive before I buy a new phone and finish it up... #boycottgenshin by the way, dont link any personal to a game.. pls.. gamer..."

## characters 
summary(nchar(genshin_reviews$TWEET))

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    15.0    65.0   109.0   131.8   193.0   632.0

## words 
summary(str_count(string = genshin_reviews$TWEET,pattern = '\\S+'))

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1.00    8.00   16.00   19.86   30.00   61.00

## sentences
summary(str_count(string = genshin_reviews$TWEET,
                  pattern = "[A-Za-z,;'\"\\s]+[^.!?]*[.?!]"))

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   0.000   1.000   1.282   2.000  11.000

## shortest reviews 
genshin_reviews$TWEET[which.min(str_count(string = genshin_reviews$TWEET,
                                          pattern = '\\S+'))]

## [1] "#boycottgenshin"

## longest reviews 
genshin_reviews$TWEET[which.max(str_count(string = genshin_reviews$TWEET,
                                          pattern = '\\S+'))]

## [1] "#BOYCOTTGENSHIN I want Tartaglia to fuck the everloving shit out of me so fucking bad. I want to drink his sweat, lick his armpits, get a face full of his pubes and have him sit on and fart in my face. I want him to pin me against a wall and have him fuck me till beg him to stop. https://t.co/44cM1D0NlL"

## common words, excluding stop words
genshin_reviews%>%
  unnest_tokens(input = TWEET, output = word)%>%
  select(word)%>%
  filter(!str_detect(word, "^http|^https|t\\.co")) %>%
  anti_join(stop_words)%>%
  group_by(word)%>%
  summarize(count = n())%>%
  ungroup()%>%
  arrange(desc(count))%>%
  top_n(10)

## Joining with `by = join_by(word)`
## Selecting by count

## # A tibble: 10 × 2
##    word                 count
##    <chr>                <int>
##  1 boycottgenshin        6752
##  2 boycottgenshinimpact  3248
##  3 game                  2151
##  4 people                1639
##  5 genshin               1253
##  6 mihoyo                 716
##  7 play                   579
##  8 shit                   526
##  9 fuck                   510
## 10 fucking                493

After scraping all the raw data for each character’s comment reviews on Genshin Impact’s Fandom Wiki page in python, a combined comment data csv file is generated for the use of comment sentiment analysis

# file paths for all character comment data and combined into one file

#file_paths <- paste0("/Users/talia/Desktop/infos/columbia/5205r-ml/comments_data_", 0:79, ".csv")
#list_of_dataframes <- lapply(file_paths, read.csv, stringsAsFactors = FALSE)
#combined_dataframe <- do.call(rbind, list_of_dataframes)
#write.csv(combined_dataframe, "/Users/talia/Desktop/infos/columbia/5205r-ml/combined_comments_data.csv", row.names = FALSE)

#file paths to read
wiki_comments = read.csv("comments_data.csv")
char_data = read.csv("5205 project data - main.csv")
banner_char = read.csv("df_characters.csv")

In terms of the analysis over the player reviews on characters, the two datasets - rev_by_charac and review_combine, which are scraped from paimon.moe and used both individually and interactively, were implemented. The final review_combine dataset contains 4 columns such as user,time, text, character, along with 57362 observations. This corresponds to 80 game characters. The final rev_by_charac dataset includes 3 columns (five_star_characters,revenue, banner_days) and 50 rows. To understand more about the relationship between the users’ reviews and the total revenues of each character, these two datasets are combined by filtering the characters in review_combine dataset with the ones also appearing in rev_by_charac dataset. So the new dataset only contains the information of 16 five-star characters.

The source of character-focus datasets is paimon.moe which is one of the most famous user-favored platform providing comprehensive statistics, such as ‘items’, ‘achievements’, ‘furnishing’, ‘weapons’, ‘reviews’,etc., and tailored service for players including ‘wish counter’, ‘calculator’, and ‘todo list’. As a popular third party user-based platform, it aligns with reality, accuracy and real time, which provides us with reliable project datasets support.

library(readr)
data<- read_csv("Review_Combined.csv")

## Rows: 57362 Columns: 4
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (4): user, time, text, character
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

revenue_data_fivestar <- read_csv("modified_Genshin_charac_rev_by_charac.csv")

## Rows: 50 Columns: 14
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (4): version_name, start_date, end_date, five_star_characters
## dbl (3): version, rerun, banner_days
## num (2): revenue, avg_revenue
## lgl (5): Unnamed: 9, Unnamed: 10, Unnamed: 11, Unnamed: 12, Unnamed: 13
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

all_fivestardata <- read_csv("Genshin_Impact_5_Star_Characters.csv")

## Rows: 27 Columns: 1
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): 5-Star Characters
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

summary(data)

##      user               time               text            character        
##  Length:57362       Length:57362       Length:57362       Length:57362      
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character

summary(revenue_data_fivestar)

##     version      version_name        start_date          end_date        
##  Min.   :1.000   Length:50          Length:50          Length:50         
##  1st Qu.:1.525   Class :character   Class :character   Class :character  
##  Median :2.400   Mode  :character   Mode  :character   Mode  :character  
##  Mean   :2.224                                                           
##  3rd Qu.:2.775                                                           
##  Max.   :3.200                                                           
##  five_star_characters     rerun         revenue          banner_days   
##  Length:50            Min.   :0.00   Min.   : 6965445   Min.   :13.00  
##  Class :character     1st Qu.:0.00   1st Qu.:13209854   1st Qu.:19.25  
##  Mode  :character     Median :1.00   Median :16804308   Median :21.00  
##                       Mean   :0.78   Mean   :18736046   Mean   :20.68  
##                       3rd Qu.:1.00   3rd Qu.:24808479   3rd Qu.:22.00  
##                       Max.   :3.00   Max.   :35939066   Max.   :43.00  
##   avg_revenue      Unnamed: 9     Unnamed: 10    Unnamed: 11    Unnamed: 12   
##  Min.   : 319135   Mode:logical   Mode:logical   Mode:logical   Mode:logical  
##  1st Qu.: 684020   NA's:50        NA's:50        NA's:50        NA's:50       
##  Median : 826672                                                              
##  Mean   : 919334                                                              
##  3rd Qu.:1131051                                                              
##  Max.   :2140130                                                              
##  Unnamed: 13   
##  Mode:logical  
##  NA's:50       
##                
##                
##                
##

summary(all_fivestardata)

##  5-Star Characters 
##  Length:27         
##  Class :character  
##  Mode  :character

B. Character Revenue Analysis

The dataset is formatted using web scraped open data on characters’ features from Genshin fandom wiki page and revenue details from Genshinlab. Upon a cursory analysis of the data, we discovered that the “rev” data frame contains an abundance of intricate information regarding 5-star characters in “Genshin Impact,” which is crucial for comprehending the factors that contribute to their revenue generating. The final structured dataset contains 50 rows with 36 columns, including:

Revenue figure: The “revenue” column displays the aggregate income made by each character during specific time periods that align with their availability in the game’s “banner” events (shown by the rerun time in the dataset).
Feature description: The features of each character include their demographic background (such as region, vision, constellation, and birthday), aesthetic features (such as hair color, eye color, and model), skill information (including weapon type, ascension, and statistics for attack, defense, and HP level), and even voice actor

Overall, this rev data frame provides a robust framework for analysis, aligning well with the problem statement’s aim to uncover insights into character revenue generation and character features. It captures not just the financial aspect but also the multifaceted elements that contribute to a character’s popularity, including gameplay mechanics, aesthetics, and scarcity. This level of detail is suitable for statistical modeling and can help developers understand the complex relationship between character features and player spending, guiding targeted enhancements to both character design and game content for increased player satisfaction and revenue generation.

##Import 5-star characters' revenue and features data
rev = read.csv("sort by rev.csv", stringsAsFactors = F)
sum(is.na(rev))

## [1] 0

head(rev)

##   id     character_name rerun    revenue rarity  region  vision weapon_type
## 1  1     Kamisato Ayaka     1 35,939,066      5 Inazuma    Cryo       Sword
## 2  2      Raiden Shogun     1 33,560,259      5 Inazuma Electro     Polearm
## 3  3 Sangonomiya Kokomi     1 33,560,259      5 Inazuma   Hydro    Catalyst
## 4  4      Raiden Shogun     0 33,020,905      5 Inazuma Electro     Polearm
## 5  5             Nahida     0 32,101,943      5  Sumeru  Dendro    Catalyst
## 6  6            Yoimiya     2 32,101,943      5 Inazuma    Pyro         Bow
##           model       constellation birthday         special_dish
## 1 Medium Female          Grus Nivis   28-Sep "Snow on the Hearth"
## 2   Tall Female  Imperatrix Umbrosa   26-Jun                 None
## 3 Medium Female Dracanea Somnolenta   22-Feb A Stunning Stratagem
## 4   Tall Female  Imperatrix Umbrosa   26-Jun                 None
## 5  Short Female Sapientia Oromasdis   27-Oct            Halvamazd
## 6 Medium Female   Carassius Auratus   21-Jun Summer Festival Fish
##            affiliation release_date limited               voice_eng  voice_cn
## 1   Yashiro Commission    2021/7/21    TRUE            Erica Mendez   Xiao N 
## 2         Inazuma City     2021/9/1    TRUE              Anne Yatco Juhuahua 
## 3     Watatsumi Island    2021/9/21    TRUE                Risa Mei Guiniang 
## 4         Inazuma City     2021/9/1    TRUE              Anne Yatco Juhuahua 
## 5          Sumeru City    2022/11/2    TRUE Kimberley Anne Campbell  Hualing 
## 6 Naganohara Fireworks    2021/8/10    TRUE          Jenny Yokobori   Na Jin 
##            voice_jp       voice_kr         ascension ascension_specialty
## 1     Saori Hayami      Lee Yu-ri           CRIT DMG        Sakura Bloom
## 2 Miyuki Sawashiro   Park Ji-yoon    Energy Recharge       Amakumo Fruit
## 3    Suzuko Mimori     Yeo Yun-mi    Hydro DMG Bonus         Sango Pearl
## 4 Miyuki Sawashiro   Park Ji-yoon    Energy Recharge       Amakumo Fruit
## 5    Tamura Yukari  Park Shi-Yoon  Elemental Mastery     Kalpalata Lotus
## 6        Kana Ueda    Bak Sin-hee          CRIT Rate           Naku Weed
##   ascension_material    ascension_boss talent_material         talent_book_1.2
## 1      Old Handguard   Perpetual Heart   Old Handguard   Teachings of Elegance
## 2      Old Handguard       Storm Beads   Old Handguard      Teachings of Light
## 3      Spectral Husk Dew of Repudation   Spectral Husk Teachings of Transience
## 4      Old Handguard       Storm Beads   Old Handguard      Teachings of Light
## 5      Fungal Spores   Quelled Creeper   Fungal Spores  Teachings of Ingenuity
## 6    Divining Scroll  Smoldering Pearl Divining Scroll Teachings of Transience
##       talent_book_2.3     talent_book_3.4     talent_book_4.5
## 1   Guide to Elegance   Guide to Elegance   Guide to Elegance
## 2      Guide to Light      Guide to Light      Guide to Light
## 3 Guide to Transience Guide to Transience Guide to Transience
## 4      Guide to Light      Guide to Light      Guide to Light
## 5  Guide to Ingenuity  Guide to Ingenuity  Guide to Ingenuity
## 6 Guide to Transience Guide to Transience Guide to Transience
##       talent_book_5.6            talent_book_6.7            talent_book_7.8
## 1   Guide to Elegance   Philosophies of Elegance   Philosophies of Elegance
## 2      Guide to Light      Philosophies of Light      Philosophies of Light
## 3 Guide to Transience Philosophies of Transience Philosophies of Transience
## 4      Guide to Light      Philosophies of Light      Philosophies of Light
## 5  Guide to Ingenuity  Philosophies of Ingenuity  Philosophies of Ingenuity
## 6 Guide to Transience Philosophies of Transience Philosophies of Transience
##              talent_book_8.9           talent_book_9.10       talent_weekly
## 1   Philosophies of Elegance   Philosophies of Elegance    Bloodjade Branch
## 2      Philosophies of Light      Philosophies of Light       Molten Moment
## 3 Philosophies of Transience Philosophies of Transience  Hellfire Butterfly
## 4      Philosophies of Light      Philosophies of Light       Molten Moment
## 5  Philosophies of Ingenuity  Philosophies of Ingenuity      Puppet Strings
## 6 Philosophies of Transience Philosophies of Transience Dragon Lord's Crown
##   max_ascencion_hp max_ascencion_atk max_ascencion_def max_lv_hp max_lv_atk
## 1         4228.035          80.28111          280.0980    13,225        251
## 2         4267.184         100.16024          249.8769    13,348        313
## 3         3484.214          74.77612          216.2160    10,898        233
## 4         2838.263          66.90411          180.1800     9,461        223
## 5         4110.590          72.63529          306.6336    12,858        227
## 6         4267.184          61.54885          159.7050    13,348        192
##   max_lv_def   base_hp base_atk base_def special_0 special_1 special_2
## 1        876 1029.5856 19.55100 68.20620     0.00%     0.00%     7.20%
## 2        781 1039.1188 24.39220 60.84711     0.00%     0.00%     7.20%
## 3        676  848.4548 18.21036 52.65040     0.00%     0.00%     7.20%
## 4        600  793.2582 18.69840 50.35800     0.00%     0.00%     6.00%
## 5        959 1000.9860 17.68900 74.66784     0.00%     0.00%     4.80%
## 6        499 1039.1188 14.98910 38.88950     0.00%     0.00%     7.20%
##   special_3 special_4 special_5 special_6 max_num_normal_atk hair_color
## 1    14.40%    14.40%    21.60%    28.80%                  5       blue
## 2    14.40%    14.40%    21.60%    28.80%                  5     purple
## 3    14.40%    14.40%    21.60%    28.80%                  3       pink
## 4    12.00%    12.00%    18.00%    24.00%                  5     purple
## 5     9.60%     9.60%    14.40%    19.20%                  4      green
## 6    14.40%    14.40%    21.60%    28.80%                  5     blonde
##   eye_color
## 1      blue
## 2    purple
## 3      blue
## 4    purple
## 5     green
## 6    golden

##Structure of variables
str(rev)

## 'data.frame':    50 obs. of  53 variables:
##  $ id                 : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ character_name     : chr  "Kamisato Ayaka" "Raiden Shogun" "Sangonomiya Kokomi" "Raiden Shogun" ...
##  $ rerun              : int  1 1 1 0 0 2 0 2 1 0 ...
##  $ revenue            : chr  "35,939,066" "33,560,259" "33,560,259" "33,020,905" ...
##  $ rarity             : int  5 5 5 5 5 5 5 5 5 5 ...
##  $ region             : chr  "Inazuma" "Inazuma" "Inazuma" "Inazuma" ...
##  $ vision             : chr  "Cryo" "Electro" "Hydro" "Electro" ...
##  $ weapon_type        : chr  "Sword" "Polearm" "Catalyst" "Polearm" ...
##  $ model              : chr  "Medium Female" "Tall Female" "Medium Female" "Tall Female" ...
##  $ constellation      : chr  "Grus Nivis" "Imperatrix Umbrosa" "Dracanea Somnolenta" "Imperatrix Umbrosa" ...
##  $ birthday           : chr  "28-Sep" "26-Jun" "22-Feb" "26-Jun" ...
##  $ special_dish       : chr  "\"Snow on the Hearth\"" "None" "A Stunning Stratagem" "None" ...
##  $ affiliation        : chr  "Yashiro Commission" "Inazuma City" "Watatsumi Island" "Inazuma City" ...
##  $ release_date       : chr  "2021/7/21" "2021/9/1" "2021/9/21" "2021/9/1" ...
##  $ limited            : logi  TRUE TRUE TRUE TRUE TRUE TRUE ...
##  $ voice_eng          : chr  "Erica Mendez" "Anne Yatco" "Risa Mei" "Anne Yatco" ...
##  $ voice_cn           : chr  "Xiao N " "Juhuahua " "Guiniang " "Juhuahua " ...
##  $ voice_jp           : chr  "Saori Hayami " "Miyuki Sawashiro " "Suzuko Mimori " "Miyuki Sawashiro " ...
##  $ voice_kr           : chr  "Lee Yu-ri " "Park Ji-yoon " "Yeo Yun-mi " "Park Ji-yoon " ...
##  $ ascension          : chr  "CRIT DMG" "Energy Recharge" "Hydro DMG Bonus" "Energy Recharge" ...
##  $ ascension_specialty: chr  "Sakura Bloom" "Amakumo Fruit" "Sango Pearl" "Amakumo Fruit" ...
##  $ ascension_material : chr  "Old Handguard" "Old Handguard" "Spectral Husk" "Old Handguard" ...
##  $ ascension_boss     : chr  "Perpetual Heart" "Storm Beads" "Dew of Repudation" "Storm Beads" ...
##  $ talent_material    : chr  "Old Handguard" "Old Handguard" "Spectral Husk" "Old Handguard" ...
##  $ talent_book_1.2    : chr  "Teachings of Elegance" "Teachings of Light" "Teachings of Transience" "Teachings of Light" ...
##  $ talent_book_2.3    : chr  "Guide to Elegance" "Guide to Light" "Guide to Transience" "Guide to Light" ...
##  $ talent_book_3.4    : chr  "Guide to Elegance" "Guide to Light" "Guide to Transience" "Guide to Light" ...
##  $ talent_book_4.5    : chr  "Guide to Elegance" "Guide to Light" "Guide to Transience" "Guide to Light" ...
##  $ talent_book_5.6    : chr  "Guide to Elegance" "Guide to Light" "Guide to Transience" "Guide to Light" ...
##  $ talent_book_6.7    : chr  "Philosophies of Elegance" "Philosophies of Light" "Philosophies of Transience" "Philosophies of Light" ...
##  $ talent_book_7.8    : chr  "Philosophies of Elegance" "Philosophies of Light" "Philosophies of Transience" "Philosophies of Light" ...
##  $ talent_book_8.9    : chr  "Philosophies of Elegance" "Philosophies of Light" "Philosophies of Transience" "Philosophies of Light" ...
##  $ talent_book_9.10   : chr  "Philosophies of Elegance" "Philosophies of Light" "Philosophies of Transience" "Philosophies of Light" ...
##  $ talent_weekly      : chr  "Bloodjade Branch" "Molten Moment" "Hellfire Butterfly" "Molten Moment" ...
##  $ max_ascencion_hp   : num  4228 4267 3484 2838 4111 ...
##  $ max_ascencion_atk  : num  80.3 100.2 74.8 66.9 72.6 ...
##  $ max_ascencion_def  : num  280 250 216 180 307 ...
##  $ max_lv_hp          : chr  "13,225" "13,348" "10,898" "9,461" ...
##  $ max_lv_atk         : int  251 313 233 223 227 192 159 225 191 212 ...
##  $ max_lv_def         : int  876 781 676 600 959 499 668 648 771 682 ...
##  $ base_hp            : num  1030 1039 848 793 1001 ...
##  $ base_atk           : num  19.6 24.4 18.2 18.7 17.7 ...
##  $ base_def           : num  68.2 60.8 52.7 50.4 74.7 ...
##  $ special_0          : chr  "0.00%" "0.00%" "0.00%" "0.00%" ...
##  $ special_1          : chr  "0.00%" "0.00%" "0.00%" "0.00%" ...
##  $ special_2          : chr  "7.20%" "7.20%" "7.20%" "6.00%" ...
##  $ special_3          : chr  "14.40%" "14.40%" "14.40%" "12.00%" ...
##  $ special_4          : chr  "14.40%" "14.40%" "14.40%" "12.00%" ...
##  $ special_5          : chr  "21.60%" "21.60%" "21.60%" "18.00%" ...
##  $ special_6          : chr  "28.80%" "28.80%" "28.80%" "24.00%" ...
##  $ max_num_normal_atk : int  5 5 3 5 4 5 6 6 6 4 ...
##  $ hair_color         : chr  "blue" "purple" "pink" "purple" ...
##  $ eye_color          : chr  "blue" "purple" "blue" "purple" ...

After examining the structure of the rev data frame, it is evident that there are many character variables present in our dataset. The next step is to convert them into appropriate data type. Initially, we convert the variables revenue, max_lv_hp, special_0 to special_6 into a numeric data type. Next, we assign new labels to the rerun variable, replacing the numbers 0 to 3 with the letters a to d. This allows us to assess the impact of character’s each rerun time on revenue. Following that, we partition the initial birthday data into the birth month and birth day. Additionally, we extract the release year of each character to be utilized in subsequent regression analysis. At last, the model column encompasses the height and gender of both characters. Therefore, it is necessary to separate them into two distinct columns: size and gender.

#Convert revenue into numeric
rev$revenue <- gsub(",", "", rev$revenue)
rev$revenue <- as.numeric(rev$revenue)

#Convert max_lv_hp into numeric
rev$max_lv_hp <- gsub(",", "", rev$max_lv_hp)
rev$max_lv_hp <- as.numeric(rev$max_lv_hp)

#Convert speical stat into numeric
special_cols <- grep("special_", names(rev), value = TRUE)
special_cols <- special_cols[!grepl("special_dish", special_cols)]
rev[special_cols] <- sapply(rev[special_cols], function(x) as.numeric(gsub("%", "", x)) / 100)

#Relabel rerun variable
rev <- rev %>%
  mutate(rerun = case_when(
    rerun == 0 ~ "a",
    rerun == 1 ~ "b",
    rerun == 2 ~ "c",
    rerun == 3 ~ "d",
    TRUE ~ as.character(rerun)))

#Convert date of birth into birth month and birth day columns
rev <- rev %>% 
  mutate(rev, 
         birthmonth = sub("\\d+-", "", birthday),
         birthday = paste0(gsub("\\D", "", birthday)))

#Convert release date into release year and release month columns
rev$release_date = as.Date(rev$release_date, format = "%Y/%m/%d")
rev <- rev %>% 
  mutate(release_year = year(release_date)) %>% 
  select(-release_date)

#Separate model type
rev <- rev %>%
  separate(model, into = c("size", "gender"), sep = " ")

#Recheck data type
str(rev)

## 'data.frame':    50 obs. of  55 variables:
##  $ id                 : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ character_name     : chr  "Kamisato Ayaka" "Raiden Shogun" "Sangonomiya Kokomi" "Raiden Shogun" ...
##  $ rerun              : chr  "b" "b" "b" "a" ...
##  $ revenue            : num  35939066 33560259 33560259 33020905 32101943 ...
##  $ rarity             : int  5 5 5 5 5 5 5 5 5 5 ...
##  $ region             : chr  "Inazuma" "Inazuma" "Inazuma" "Inazuma" ...
##  $ vision             : chr  "Cryo" "Electro" "Hydro" "Electro" ...
##  $ weapon_type        : chr  "Sword" "Polearm" "Catalyst" "Polearm" ...
##  $ size               : chr  "Medium" "Tall" "Medium" "Tall" ...
##  $ gender             : chr  "Female" "Female" "Female" "Female" ...
##  $ constellation      : chr  "Grus Nivis" "Imperatrix Umbrosa" "Dracanea Somnolenta" "Imperatrix Umbrosa" ...
##  $ birthday           : chr  "28" "26" "22" "26" ...
##  $ special_dish       : chr  "\"Snow on the Hearth\"" "None" "A Stunning Stratagem" "None" ...
##  $ affiliation        : chr  "Yashiro Commission" "Inazuma City" "Watatsumi Island" "Inazuma City" ...
##  $ limited            : logi  TRUE TRUE TRUE TRUE TRUE TRUE ...
##  $ voice_eng          : chr  "Erica Mendez" "Anne Yatco" "Risa Mei" "Anne Yatco" ...
##  $ voice_cn           : chr  "Xiao N " "Juhuahua " "Guiniang " "Juhuahua " ...
##  $ voice_jp           : chr  "Saori Hayami " "Miyuki Sawashiro " "Suzuko Mimori " "Miyuki Sawashiro " ...
##  $ voice_kr           : chr  "Lee Yu-ri " "Park Ji-yoon " "Yeo Yun-mi " "Park Ji-yoon " ...
##  $ ascension          : chr  "CRIT DMG" "Energy Recharge" "Hydro DMG Bonus" "Energy Recharge" ...
##  $ ascension_specialty: chr  "Sakura Bloom" "Amakumo Fruit" "Sango Pearl" "Amakumo Fruit" ...
##  $ ascension_material : chr  "Old Handguard" "Old Handguard" "Spectral Husk" "Old Handguard" ...
##  $ ascension_boss     : chr  "Perpetual Heart" "Storm Beads" "Dew of Repudation" "Storm Beads" ...
##  $ talent_material    : chr  "Old Handguard" "Old Handguard" "Spectral Husk" "Old Handguard" ...
##  $ talent_book_1.2    : chr  "Teachings of Elegance" "Teachings of Light" "Teachings of Transience" "Teachings of Light" ...
##  $ talent_book_2.3    : chr  "Guide to Elegance" "Guide to Light" "Guide to Transience" "Guide to Light" ...
##  $ talent_book_3.4    : chr  "Guide to Elegance" "Guide to Light" "Guide to Transience" "Guide to Light" ...
##  $ talent_book_4.5    : chr  "Guide to Elegance" "Guide to Light" "Guide to Transience" "Guide to Light" ...
##  $ talent_book_5.6    : chr  "Guide to Elegance" "Guide to Light" "Guide to Transience" "Guide to Light" ...
##  $ talent_book_6.7    : chr  "Philosophies of Elegance" "Philosophies of Light" "Philosophies of Transience" "Philosophies of Light" ...
##  $ talent_book_7.8    : chr  "Philosophies of Elegance" "Philosophies of Light" "Philosophies of Transience" "Philosophies of Light" ...
##  $ talent_book_8.9    : chr  "Philosophies of Elegance" "Philosophies of Light" "Philosophies of Transience" "Philosophies of Light" ...
##  $ talent_book_9.10   : chr  "Philosophies of Elegance" "Philosophies of Light" "Philosophies of Transience" "Philosophies of Light" ...
##  $ talent_weekly      : chr  "Bloodjade Branch" "Molten Moment" "Hellfire Butterfly" "Molten Moment" ...
##  $ max_ascencion_hp   : num  4228 4267 3484 2838 4111 ...
##  $ max_ascencion_atk  : num  80.3 100.2 74.8 66.9 72.6 ...
##  $ max_ascencion_def  : num  280 250 216 180 307 ...
##  $ max_lv_hp          : num  13225 13348 10898 9461 12858 ...
##  $ max_lv_atk         : int  251 313 233 223 227 192 159 225 191 212 ...
##  $ max_lv_def         : int  876 781 676 600 959 499 668 648 771 682 ...
##  $ base_hp            : num  1030 1039 848 793 1001 ...
##  $ base_atk           : num  19.6 24.4 18.2 18.7 17.7 ...
##  $ base_def           : num  68.2 60.8 52.7 50.4 74.7 ...
##  $ special_0          : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ special_1          : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ special_2          : num  0.072 0.072 0.072 0.06 0.048 0.072 0.06 0.072 0.067 0.06 ...
##  $ special_3          : num  0.144 0.144 0.144 0.12 0.096 0.144 0.12 0.144 0.133 0.12 ...
##  $ special_4          : num  0.144 0.144 0.144 0.12 0.096 0.144 0.12 0.144 0.133 0.12 ...
##  $ special_5          : num  0.216 0.216 0.216 0.18 0.144 0.216 0.18 0.216 0.2 0.18 ...
##  $ special_6          : num  0.288 0.288 0.288 0.24 0.192 0.288 0.24 0.288 0.267 0.24 ...
##  $ max_num_normal_atk : int  5 5 3 5 4 5 6 6 6 4 ...
##  $ hair_color         : chr  "blue" "purple" "pink" "purple" ...
##  $ eye_color          : chr  "blue" "purple" "blue" "purple" ...
##  $ birthmonth         : chr  "Sep" "Jun" "Feb" "Jun" ...
##  $ release_year       : num  2021 2021 2021 2021 2022 ...

#Standardize numeric explanatory variable and check missing value
head(rev)

##   id     character_name rerun  revenue rarity  region  vision weapon_type
## 1  1     Kamisato Ayaka     b 35939066      5 Inazuma    Cryo       Sword
## 2  2      Raiden Shogun     b 33560259      5 Inazuma Electro     Polearm
## 3  3 Sangonomiya Kokomi     b 33560259      5 Inazuma   Hydro    Catalyst
## 4  4      Raiden Shogun     a 33020905      5 Inazuma Electro     Polearm
## 5  5             Nahida     a 32101943      5  Sumeru  Dendro    Catalyst
## 6  6            Yoimiya     c 32101943      5 Inazuma    Pyro         Bow
##     size gender       constellation birthday         special_dish
## 1 Medium Female          Grus Nivis       28 "Snow on the Hearth"
## 2   Tall Female  Imperatrix Umbrosa       26                 None
## 3 Medium Female Dracanea Somnolenta       22 A Stunning Stratagem
## 4   Tall Female  Imperatrix Umbrosa       26                 None
## 5  Short Female Sapientia Oromasdis       27            Halvamazd
## 6 Medium Female   Carassius Auratus       21 Summer Festival Fish
##            affiliation limited               voice_eng  voice_cn
## 1   Yashiro Commission    TRUE            Erica Mendez   Xiao N 
## 2         Inazuma City    TRUE              Anne Yatco Juhuahua 
## 3     Watatsumi Island    TRUE                Risa Mei Guiniang 
## 4         Inazuma City    TRUE              Anne Yatco Juhuahua 
## 5          Sumeru City    TRUE Kimberley Anne Campbell  Hualing 
## 6 Naganohara Fireworks    TRUE          Jenny Yokobori   Na Jin 
##            voice_jp       voice_kr         ascension ascension_specialty
## 1     Saori Hayami      Lee Yu-ri           CRIT DMG        Sakura Bloom
## 2 Miyuki Sawashiro   Park Ji-yoon    Energy Recharge       Amakumo Fruit
## 3    Suzuko Mimori     Yeo Yun-mi    Hydro DMG Bonus         Sango Pearl
## 4 Miyuki Sawashiro   Park Ji-yoon    Energy Recharge       Amakumo Fruit
## 5    Tamura Yukari  Park Shi-Yoon  Elemental Mastery     Kalpalata Lotus
## 6        Kana Ueda    Bak Sin-hee          CRIT Rate           Naku Weed
##   ascension_material    ascension_boss talent_material         talent_book_1.2
## 1      Old Handguard   Perpetual Heart   Old Handguard   Teachings of Elegance
## 2      Old Handguard       Storm Beads   Old Handguard      Teachings of Light
## 3      Spectral Husk Dew of Repudation   Spectral Husk Teachings of Transience
## 4      Old Handguard       Storm Beads   Old Handguard      Teachings of Light
## 5      Fungal Spores   Quelled Creeper   Fungal Spores  Teachings of Ingenuity
## 6    Divining Scroll  Smoldering Pearl Divining Scroll Teachings of Transience
##       talent_book_2.3     talent_book_3.4     talent_book_4.5
## 1   Guide to Elegance   Guide to Elegance   Guide to Elegance
## 2      Guide to Light      Guide to Light      Guide to Light
## 3 Guide to Transience Guide to Transience Guide to Transience
## 4      Guide to Light      Guide to Light      Guide to Light
## 5  Guide to Ingenuity  Guide to Ingenuity  Guide to Ingenuity
## 6 Guide to Transience Guide to Transience Guide to Transience
##       talent_book_5.6            talent_book_6.7            talent_book_7.8
## 1   Guide to Elegance   Philosophies of Elegance   Philosophies of Elegance
## 2      Guide to Light      Philosophies of Light      Philosophies of Light
## 3 Guide to Transience Philosophies of Transience Philosophies of Transience
## 4      Guide to Light      Philosophies of Light      Philosophies of Light
## 5  Guide to Ingenuity  Philosophies of Ingenuity  Philosophies of Ingenuity
## 6 Guide to Transience Philosophies of Transience Philosophies of Transience
##              talent_book_8.9           talent_book_9.10       talent_weekly
## 1   Philosophies of Elegance   Philosophies of Elegance    Bloodjade Branch
## 2      Philosophies of Light      Philosophies of Light       Molten Moment
## 3 Philosophies of Transience Philosophies of Transience  Hellfire Butterfly
## 4      Philosophies of Light      Philosophies of Light       Molten Moment
## 5  Philosophies of Ingenuity  Philosophies of Ingenuity      Puppet Strings
## 6 Philosophies of Transience Philosophies of Transience Dragon Lord's Crown
##   max_ascencion_hp max_ascencion_atk max_ascencion_def max_lv_hp max_lv_atk
## 1         4228.035          80.28111          280.0980     13225        251
## 2         4267.184         100.16024          249.8769     13348        313
## 3         3484.214          74.77612          216.2160     10898        233
## 4         2838.263          66.90411          180.1800      9461        223
## 5         4110.590          72.63529          306.6336     12858        227
## 6         4267.184          61.54885          159.7050     13348        192
##   max_lv_def   base_hp base_atk base_def special_0 special_1 special_2
## 1        876 1029.5856 19.55100 68.20620         0         0     0.072
## 2        781 1039.1188 24.39220 60.84711         0         0     0.072
## 3        676  848.4548 18.21036 52.65040         0         0     0.072
## 4        600  793.2582 18.69840 50.35800         0         0     0.060
## 5        959 1000.9860 17.68900 74.66784         0         0     0.048
## 6        499 1039.1188 14.98910 38.88950         0         0     0.072
##   special_3 special_4 special_5 special_6 max_num_normal_atk hair_color
## 1     0.144     0.144     0.216     0.288                  5       blue
## 2     0.144     0.144     0.216     0.288                  5     purple
## 3     0.144     0.144     0.216     0.288                  3       pink
## 4     0.120     0.120     0.180     0.240                  5     purple
## 5     0.096     0.096     0.144     0.192                  4      green
## 6     0.144     0.144     0.216     0.288                  5     blonde
##   eye_color birthmonth release_year
## 1      blue        Sep         2021
## 2    purple        Jun         2021
## 3      blue        Feb         2021
## 4    purple        Jun         2021
## 5     green        Oct         2022
## 6    golden        Jun         2021

rev[, 35:50] <- scale(rev[, 35:50])
rev <- rev %>% select(-special_0, -special_1)
sum(is.na(rev))

## [1] 0

C. Time Series - Weapons Event Revenue Analysis

To construct a dataset to conduct the time series analysis was a two step procurement process. The first step was web scraping Paimon.moe, a Genshin Impact database, using Python. The data collected was the name of each five star weapon, the total number of people who pulled that weapon, and the event name. Since the team did not have access to the actual revenue amount an estimate can be deducted from the amount of pulls from each event. This is because the more people who are rolling for new weapons means that Genshin Impact will see an increase in revenue as a result. The next step was finding the dates for each event and appending that to match the event in the data collected in part one.After finding a historical weapons event calendar on the Genshin Impact Wiki and web scraping the data it was appended to the original dataset.

The data was then aggregated by event and summed to get the number of pulls for each event. The time of each event was approximately three weeks or 17 events a year. This dataset had the best characteristics to conduct time series analysis with events that were evenly spaced out throughout the year and totals to forecast the revenue for future events.

##Import TS Weapons Data and create TS object

ts_weapons <- read_csv("ts_weapons.csv")

## Rows: 54 Columns: 4
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr  (1): Event
## dbl  (1): Total
## date (2): Start, End
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

ts_weapons$Start <- as.Date(ts_weapons$Start)
ts_weapons$End <- as.Date(ts_weapons$End)

xts_data <- xts(ts_weapons$Total, order.by = ts_weapons$Start)

ts_data <- ts(xts_data, start = 2021, frequency = 17)  # By Amount of Events a Year
plot(ts_data)

Analysis Methods

A. Text Mining - Sentiment Analysis

The choice of sentiment analysis as the analytical technique is not only well-suited for the research question, but also highly relevant in the context of the gaming industry. Sentiment analysis allows for systematically examining opinions, attitudes, and emotions expressed in text data, making it an appropriate method for exploring customer sentiments in our dataset.

Multiple lexicons are employed for the analysis: Binary Sentiment, NRC Emotion, AFINN, and Jockers. Each lexicon offers unique advantages and provides a different perspective on the data. The binary lexicon serves as a starting point, broadly classifying sentiments into positive and negative categories. This high-level overview helps gauge the overall sentiment landscape and provides a foundation for further analysis. For instance, the NRC emotion lexicon is utilized to develop deeper insights into players’ emotions. This lexicon identifies and quantifies specific emotions such as joy, anger, sadness, and fear. By analyzing the frequency and spread of these emotions, one can better understand the complex and diverse user sentiments regarding Genshin Impact.

Moreover, the AFINN lexicon assesses sentiment polarity, providing a numerical score for each tweet. This quantitative measure allows for identifying strongly positive or negative sentiments and facilitates the comparison of sentiment intensity across different tweets. By leveraging the AFINN lexicon, trends and patterns in sentiment polarity can be uncovered. Finally, the Jockers lexicon is incorporated to account for the sentiment analysis’s context and parts of speech (POS). This lexicon considers the surrounding words and their grammatical roles, enabling a more comprehensive interpretation of sentiments.

#Tokenize words
# One word 
# Create an id column 
genshin_reviews <- genshin_reviews %>% 
  mutate(id = row_number()) %>% 
  select(id, everything())

#tokenize based on word
genshin_reviews %>%
  select(id,TWEET)%>%
  group_by(id)%>%
  unnest_tokens(input = TWEET, output = word)%>%
  ungroup()%>%
  group_by(id)%>%
  summarize(count = n())

## # A tibble: 9,883 × 2
##       id count
##    <int> <int>
##  1     1     5
##  2     2    33
##  3     3    48
##  4     4    50
##  5     5    10
##  6     6    33
##  7     7    33
##  8     8     9
##  9     9     4
## 10    10     9
## # ℹ 9,873 more rows

#Exclude dirty words
#profanity_alvarez
#profanity_arr_bad
#profanity_banned
#profanity_racist
#profanity_zac_anger

genshin_reviews <-genshin_reviews %>%
  group_by(id)%>%
  unnest_tokens(output = word, input = TWEET)%>%
  ungroup()%>%
  select(id, word)%>%
  anti_join(data.frame(word = c(profanity_banned, profanity_racist, profanity_alvarez,
                                profanity_arr_bad, profanity_zac_anger)), 
            by = c('word'='word'))

#Change the column name to TWEET
colnames(genshin_reviews)[2] = "TWEET"

Binary Sentiment Model

Model for review over the whole game

# Binary Token
genshin_reviews_bin <- genshin_reviews %>% 
  select(id,TWEET) %>% 
  group_by(id)%>%
  unnest_tokens(input = TWEET, output = word)%>%
  inner_join(get_sentiments('bing'))%>%
  group_by(sentiment)

## Joining with `by = join_by(word)`

Model for review over the characters

library('tidytext');
library(tidyr); library(dplyr); library(ggplot2); library(ggthemes)
sentiment_fullcharacter<-data %>%
  unnest_tokens(word, text) %>%
  inner_join(get_sentiments("bing")) %>%
  count(character, sentiment) %>%
  spread(sentiment, n, fill = 0) %>%
  mutate(total = positive + negative,
         prop_positive = positive / total,
         prop_negative = negative / total) %>%
  arrange(desc(prop_positive))

## Joining with `by = join_by(word)`

## Warning in inner_join(., get_sentiments("bing")): Detected an unexpected many-to-many relationship between `x` and `y`.
## ℹ Row 232508 of `x` matches multiple rows in `y`.
## ℹ Row 3857 of `y` matches multiple rows in `x`.
## ℹ If a many-to-many relationship is expected, set `relationship =
##   "many-to-many"` to silence this warning.

NRC Emotion Sentiment Model

## install and explore the nrc package 
nrc = get_sentiments('nrc')

nrc %>% 
  group_by(sentiment) %>% 
  count()

## # A tibble: 10 × 2
## # Groups:   sentiment [10]
##    sentiment        n
##    <chr>        <int>
##  1 anger         1245
##  2 anticipation   837
##  3 disgust       1056
##  4 fear          1474
##  5 joy            687
##  6 negative      3316
##  7 positive      2308
##  8 sadness       1187
##  9 surprise       532
## 10 trust         1230

##Perform sentiment analysis 
genshin_reviews_nrc_emotion <- genshin_reviews %>% 
  select(id,TWEET) %>% 
  group_by(id)%>%
  unnest_tokens(output = word, input = TWEET)%>%
  inner_join(nrc, relationship = "many-to-many")%>%
  group_by(sentiment)%>%
  count() %>% 
  ungroup()

## Joining with `by = join_by(word)`

AFINN Sentiment Model

afinn = get_sentiments('afinn')

genshin_reviews_afinn <- genshin_reviews %>% 
  select(id,TWEET)%>%
  group_by(id)%>%
  unnest_tokens(output=word,input=TWEET)%>%
  inner_join(afinn)%>%
  summarize(reviewSentiment = mean(value))%>%
  ungroup()

## Joining with `by = join_by(word)`

Jockers Sentiment Model

genshin_reviews_Jockers <- genshin_reviews%>%
  select(id,TWEET) %>% 
  group_by(id)%>%
  unnest_tokens(output=word,input=TWEET)%>%
  inner_join(key_sentiment_jockers)%>%
  summarize(reviewSentiment = mean(value))%>%
  ungroup()

## Joining with `by = join_by(word)`

B. Comment data Exploration Using Time-series Analysis

Data Preperation

Though all comment data is now in one combiend csv file, the timestamp used in the scraped data set is not in uniform date format. The time format here is set for retrieval time and would be used later for all timestamps. In comment data, comment times within a week are all listed using units “d” for days, “m” for minutes, or “h” for hours, and thus have to be converted into the timestamp format used above.

#file paths to read
wiki_comments = read.csv("comments_data.csv")
char_data = read.csv("5205 project data - main.csv")
banner_char = read.csv("df_characters.csv")

#used packages for data cleaning and preparation
library(dplyr)
library(stringr)
library(lubridate)
library(ggplot2)

#timestamp format to be used 
time_retrieved <- as.Date("2024-04-07")

#function to detect and treat informal time formatting
convert_time_to_date <- function(time_string, retrieval_date) {
  parsed_date <- mdy(time_string)
  if (!is.na(parsed_date)) {
    return(parsed_date)
  }
  if (str_detect(time_string, "d$")) {
    days <- as.numeric(str_extract(time_string, "\\d+"))
    return(retrieval_date - days)
  } else if (str_detect(time_string, "[hm]$")) {
    return(retrieval_date)
  } else {
    return(NA)
  }
}

#made into uniform time format
wiki_comments <- wiki_comments %>%
  rowwise() %>%
  mutate(time = convert_time_to_date(time, time_retrieved)) %>%
  ungroup()

## Warning: There were 65 warnings in `mutate()`.
## The first warning was:
## ℹ In argument: `time = convert_time_to_date(time, time_retrieved)`.
## ℹ In row 6.
## Caused by warning:
## ! All formats failed to parse. No formats found.
## ℹ Run `dplyr::last_dplyr_warnings()` to see the 64 remaining warnings.

Basic Plots

Basic Plots could be used to provide a general idea of trends in how comment data change with time for each of the characters. The general trend is notable. For most of the characters, especially those of 5 stars, comment amount spikes (by peak_dates_all) around the days of their first release time, and then gradually converges to around 0. However, further analysis on the trends and seasonality, models could not be done without time series analysis.

#line chart, bar chart, and trendline for all characters stored as list
character_plots <- list()

for(character_name in char_data$character) {
  character_data <- wiki_comments %>%
    filter(character == character_name) %>%
    group_by(time) %>%
    summarise(Count = n())

  character_plots[[character_name]] <- ggplot(character_data, aes(x = time, y = Count)) +
    geom_line() +
    labs(title = paste("Daily Comments for", character_name),
         x = "Date",
         y = "Number of Comments") +
    theme_minimal()
  
  character_plots[[paste(character_name, "bar", sep = "_")]] <- ggplot(character_data, aes(x = time, y = Count)) +
    geom_bar(stat = "identity") +
    labs(title = paste("Daily Comments for", character_name),
         x = "Date",
         y = "Number of Comments") +
    theme_minimal()
  ggplot(character_data, aes(x = time, y = Count)) +
  geom_line() +
  geom_smooth(se = FALSE, span = 0.03) + 
  labs(title = paste("Daily Comments for", character_name),
       x = "Date",
       y = "Number of Comments") +
  theme_minimal()
}

#the local maxima and global top review amount days
peak_dates_all <- data.frame(character = character(), peak_date = character())

for(character_name in char_data$character) {
  character_month <- character_data %>%
    mutate(YearMonth = floor_date(time, unit = "quarter")) %>%
    group_by(YearMonth) %>%
    filter(Count == max(Count)) %>%
    ungroup()
  peak_dates <- character_month$time

    peak_dates_all <- rbind(peak_dates_all, data.frame(character = character_name, peak_date = peak_dates))

  character_plots[[character_name]] <- ggplot(character_month, aes(x = time, y = Count)) +
    geom_line() +
    geom_point(data = data.frame(time = peak_dates, Count = character_month$Count), 
               aes(x = time, y = Count), color = "red", size = 3) +
    labs(title = paste("Quarterly Peak Comments for", character_name),
         x = "Date",
         y = "Number of Comments") +
    theme_minimal()
}

Time Series Analysis

The characteristics of the datasets makes it in dataframae format. To begin with time series analysis, the datasets are all converted into ts format and plots for each are drawn in ts_plots list to be analyzed together. Individual analysis for each character is then performed afterwards for each of their best models and analyze for whether there are seasonality among most of the characters. The seasonal analysis could not be performed on the raw ts data since it is irregular, so an time series analysis using ttr and irts is performed first. Then the ts is converted into regular ts objects by filling up the missing date values and then a ts analysis for regular time series objects are done later. Since for some of the characters, they are released for less than 2 times of the frequency (365), seasonal naive model could not be done.Since the frequency of 365 of the current regular ts is too large for Holt’s winter analysis and ETS analysis, a bi-weekly ts is also generated, but unfortunately could only be done for part of the characters because of data point limitations (<9 bi-weeks). All models are applied to character if possible.

#packages used in time series analysis
library(ggthemes);library(gridExtra)  
library(quantmod);library(xts);library(zoo) 
library(forecast) 
library(fpp); library(fpp2) 
library(tseries) 
library("TTR")

#time series plots after converted into time series format
ts_plots <- list()

for(character_name in char_data$character) {
  character_data <- wiki_comments %>%
    filter(character == character_name) %>%
    group_by(time) %>%
    summarise(Count = n(), .groups = 'drop')  
    ts_character <- ts(character_data$Count)
  
  ts_plots[[character_name]] <- list(
    ts_object = ts_character,
    class = class(ts_character)
  )
  
  ts_plots[[character_name]]$plot <- ggplot2::qplot(seq_along(ts_character), ts_character, geom = "line") +
    labs(title = paste("Time Series for", character_name),
         x = "Time",
         y = "Count") +
    theme_minimal()
  
  plot_filename <- paste0("ts_plot_", character_name, ".png")
  ggsave(plot_filename, plot = ts_plots[[character_name]]$plot, width = 10, height = 6, dpi = 300)
  
  #print(ts_plots[[character_name]]$class)
}

## Warning: `qplot()` was deprecated in ggplot2 3.4.0.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
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## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
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## Don't know how to automatically pick scale for object of type <ts>. Defaulting
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## Don't know how to automatically pick scale for object of type <ts>. Defaulting
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## Don't know how to automatically pick scale for object of type <ts>. Defaulting
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## Don't know how to automatically pick scale for object of type <ts>. Defaulting
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## Don't know how to automatically pick scale for object of type <ts>. Defaulting
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## Don't know how to automatically pick scale for object of type <ts>. Defaulting
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## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
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## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.
## Don't know how to automatically pick scale for object of type <ts>. Defaulting
## to continuous.

character_name =char_data$character[1]
character_name

## [1] "Albedo"

character_data <- wiki_comments %>%
    filter(character == character_name) %>%
    group_by(time) %>%
    summarise(Count = n(), .groups = 'drop')
count_ts <- ts(character_data$Count)

####Irregular TS Analysis

#files for all results, accuracy, and plots are stored locally using this sample code snippet (similar codes are not kept here)

#make_filename <- function(base_name) {
#  paste0(character_name, "_", base_name, ".png")
#}
#png(make_filename("basic_ts_plot"))
#plot.ts(count_ts)
#dev.off()
#for results in console:
#file_name <- paste0(character_name, "_simple_forecasting.txt")
#sink(file_name)
#sink()
#for ggplots:
#plot_file_name <- make_filename(paste0(character_name, "_forecast_comparison_plot.png"))
#ggsave(plot_file_name, ts_plot, width = 8, height = 4, dpi = 300)


#plots are messy, thus use ttr to make it more smooth
SMA3 <- SMA(count_ts,n=3)
SMA50 <- SMA(count_ts,n=50)
SMA100 <- SMA(count_ts,n=100)# not available for some characters released recently
plot.ts(SMA3)

plot.ts(SMA50)

plot.ts(SMA100)

#acf
acf(x = count_ts,lag.max = 1,plot=F)

## 
## Autocorrelations of series 'count_ts', by lag
## 
##     0     1 
## 1.000 0.784

acf(x = count_ts,plot=F)

## 
## Autocorrelations of series 'count_ts', by lag
## 
##      0      1      2      3      4      5      6      7      8      9     10 
##  1.000  0.784  0.653  0.611  0.550  0.507  0.543  0.538  0.492  0.488  0.472 
##     11     12     13     14     15     16     17     18     19     20     21 
##  0.436  0.380  0.309  0.250  0.228  0.204  0.201  0.198  0.145  0.103  0.126 
##     22     23     24     25     26 
##  0.097  0.051  0.042  0.009 -0.037

acf(x = count_ts)

ggAcf(x = count_ts)

#the ts at first is not seasonal since no data points at all dates
numeric_times <- as.numeric(as.POSIXct(character_data$time))
my_irts <- irts(numeric_times, character_data$Count)
print(my_irts)

## 2020-10-31 00:00:00 GMT 1
## 2020-11-02 00:00:00 GMT 2
## 2020-11-03 00:00:00 GMT 2
## 2020-11-04 00:00:00 GMT 1
## 2020-11-12 00:00:00 GMT 7
## 2020-11-13 00:00:00 GMT 8
## 2020-11-15 00:00:00 GMT 4
## 2020-11-16 00:00:00 GMT 4
## 2020-11-17 00:00:00 GMT 2
## 2020-11-18 00:00:00 GMT 1
## 2020-11-19 00:00:00 GMT 3
## 2020-11-20 00:00:00 GMT 1
## 2020-11-21 00:00:00 GMT 1
## 2020-11-22 00:00:00 GMT 1
## 2020-11-24 00:00:00 GMT 5
## 2020-11-25 00:00:00 GMT 9
## 2020-11-26 00:00:00 GMT 3
## 2020-11-27 00:00:00 GMT 4
## 2020-11-29 00:00:00 GMT 1
## 2020-11-30 00:00:00 GMT 5
## 2020-12-03 00:00:00 GMT 5
## 2020-12-04 00:00:00 GMT 5
## 2020-12-05 00:00:00 GMT 3
## 2020-12-06 00:00:00 GMT 2
## 2020-12-07 00:00:00 GMT 1
## 2020-12-09 00:00:00 GMT 3
## 2020-12-11 00:00:00 GMT 18
## 2020-12-12 00:00:00 GMT 18
## 2020-12-13 00:00:00 GMT 10
## 2020-12-14 00:00:00 GMT 23
## 2020-12-15 00:00:00 GMT 21
## 2020-12-16 00:00:00 GMT 9
## 2020-12-17 00:00:00 GMT 17
## 2020-12-18 00:00:00 GMT 12
## 2020-12-19 00:00:00 GMT 6
## 2020-12-20 00:00:00 GMT 16
## 2020-12-21 00:00:00 GMT 42
## 2020-12-22 00:00:00 GMT 40
## 2020-12-23 00:00:00 GMT 54
## 2020-12-24 00:00:00 GMT 37
## 2020-12-25 00:00:00 GMT 24
## 2020-12-26 00:00:00 GMT 13
## 2020-12-27 00:00:00 GMT 20
## 2020-12-28 00:00:00 GMT 27
## 2020-12-29 00:00:00 GMT 21
## 2020-12-30 00:00:00 GMT 14
## 2020-12-31 00:00:00 GMT 10
## 2021-01-01 00:00:00 GMT 20
## 2021-01-02 00:00:00 GMT 16
## 2021-01-03 00:00:00 GMT 9
## 2021-01-04 00:00:00 GMT 15
## 2021-01-05 00:00:00 GMT 16
## 2021-01-06 00:00:00 GMT 2
## 2021-01-07 00:00:00 GMT 5
## 2021-01-08 00:00:00 GMT 15
## 2021-01-09 00:00:00 GMT 11
## 2021-01-10 00:00:00 GMT 7
## 2021-01-11 00:00:00 GMT 10
## 2021-01-12 00:00:00 GMT 6
## 2021-01-13 00:00:00 GMT 5
## 2021-01-14 00:00:00 GMT 7
## 2021-01-15 00:00:00 GMT 2
## 2021-01-16 00:00:00 GMT 1
## 2021-01-17 00:00:00 GMT 2
## 2021-01-18 00:00:00 GMT 1
## 2021-01-19 00:00:00 GMT 1
## 2021-01-20 00:00:00 GMT 3
## 2021-01-21 00:00:00 GMT 7
## 2021-01-22 00:00:00 GMT 1
## 2021-01-23 00:00:00 GMT 1
## 2021-01-24 00:00:00 GMT 4
## 2021-01-28 00:00:00 GMT 1
## 2021-01-29 00:00:00 GMT 1
## 2021-01-30 00:00:00 GMT 1
## 2021-01-31 00:00:00 GMT 2
## 2021-02-01 00:00:00 GMT 3
## 2021-02-02 00:00:00 GMT 1
## 2021-02-04 00:00:00 GMT 2
## 2021-02-06 00:00:00 GMT 4
## 2021-02-07 00:00:00 GMT 1
## 2021-02-08 00:00:00 GMT 6
## 2021-02-09 00:00:00 GMT 3
## 2021-02-12 00:00:00 GMT 2
## 2021-02-13 00:00:00 GMT 4
## 2021-02-14 00:00:00 GMT 2
## 2021-02-16 00:00:00 GMT 5
## 2021-02-17 00:00:00 GMT 1
## 2021-02-18 00:00:00 GMT 2
## 2021-02-19 00:00:00 GMT 1
## 2021-02-20 00:00:00 GMT 4
## 2021-02-21 00:00:00 GMT 1
## 2021-02-22 00:00:00 GMT 4
## 2021-02-23 00:00:00 GMT 4
## 2021-02-24 00:00:00 GMT 1
## 2021-02-25 00:00:00 GMT 2
## 2021-02-27 00:00:00 GMT 2
## 2021-03-02 00:00:00 GMT 1
## 2021-03-05 00:00:00 GMT 1
## 2021-03-08 00:00:00 GMT 5
## 2021-03-10 00:00:00 GMT 1
## 2021-03-11 00:00:00 GMT 2
## 2021-03-14 00:00:00 GMT 1
## 2021-03-15 00:00:00 GMT 4
## 2021-03-16 00:00:00 GMT 1
## 2021-03-17 00:00:00 GMT 1
## 2021-03-18 00:00:00 GMT 4
## 2021-03-19 00:00:00 GMT 2
## 2021-03-20 00:00:00 GMT 2
## 2021-03-21 00:00:00 GMT 3
## 2021-03-22 00:00:00 GMT 1
## 2021-03-23 00:00:00 GMT 3
## 2021-03-24 00:00:00 GMT 2
## 2021-03-25 00:00:00 GMT 2
## 2021-03-26 00:00:00 GMT 4
## 2021-03-27 00:00:00 GMT 2
## 2021-03-28 00:00:00 GMT 3
## 2021-03-29 00:00:00 GMT 5
## 2021-03-31 00:00:00 GMT 4
## 2021-04-01 00:00:00 GMT 1
## 2021-04-02 00:00:00 GMT 3
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## NA 1

class(my_irts)

## [1] "irts"

####Regular TS

#converting to regular ts from irregular ts
character_data$time <- as.Date(character_data$time)
valid_times <- character_data$time[!is.na(character_data$time)]
all_dates <- seq(min(valid_times), max(valid_times), by = "day")
all_dates_df <- data.frame(time = all_dates)

regular_character_data <- all_dates_df %>%
  left_join(character_data, by = "time")
regular_character_data <- regular_character_data %>%
  mutate(Count = ifelse(is.na(Count), 0, Count))

regular_ts <- ts(regular_character_data$Count, start = c(year(min(all_dates)), yday(min(all_dates))), frequency = 365)

ggseasonplot(regular_ts)

ggseasonplot(regular_ts, polar = TRUE)

stl_plot <- regular_ts %>%
  stl(s.window = 'periodic') %>%
  autoplot()

Regular TS-simple forcasting model

train_end_index <- round(length(regular_ts) * 0.7)
ts_start <- start(regular_ts)
ts_frequency <- frequency(regular_ts)

train <- window(regular_ts, end = ts_start + (train_end_index - 1)/ts_frequency)
test <- window(regular_ts, start = ts_start + train_end_index/ts_frequency)

print(length(train))

## [1] 880

print(length(test))

## [1] 373

print(start(train))

## [1] 2020  305

print(end(train))

## [1] 2023   89

print(start(test))

## [1] 2023   91

print(end(test))

## [1] 2024   98

Regular TS-average method

average_model <- meanf(train, h = length(test))
train_acc_ave <- accuracy(average_model) # Train accuracy
test_acc_ave <- accuracy(average_model, x = regular_ts) # Test accuracy

print(average_model)

##           Point Forecast   Lo 80    Hi 80     Lo 95   Hi 95
## 2023.2438       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.2466       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.2493       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.2521       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.2548       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.2575       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.2603       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.2630       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.2658       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.2685       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.2712       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.2740       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.2767       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.2795       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.2822       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.2849       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.2877       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.2904       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.2932       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.2959       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.2986       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3014       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3041       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3068       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3096       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3123       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3151       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3178       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3205       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3233       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3260       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3288       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3315       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3342       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3370       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3397       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3425       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3452       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3479       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3507       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3534       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3562       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3589       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3616       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3644       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3671       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3699       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3726       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3753       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3781       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3808       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3836       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3863       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3890       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3918       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3945       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.3973       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4000       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4027       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4055       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4082       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4110       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4137       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4164       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4192       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4219       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4247       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4274       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4301       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4329       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4356       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4384       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4411       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4438       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4466       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4493       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4521       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4548       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4575       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4603       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4630       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4658       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4685       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4712       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4740       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4767       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4795       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4822       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4849       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4877       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4904       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4932       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4959       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.4986       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5014       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5041       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5068       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5096       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5123       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5151       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5178       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5205       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5233       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5260       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5288       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5315       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5342       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5370       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5397       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5425       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5452       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5479       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5507       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5534       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5562       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5589       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5616       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5644       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5671       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5699       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5726       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5753       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5781       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5808       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5836       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5863       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5890       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5918       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5945       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.5973       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6000       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6027       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6055       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6082       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6110       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6137       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6164       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6192       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6219       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6247       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6274       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6301       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6329       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6356       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6384       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6411       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6438       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6466       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6493       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6521       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6548       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6575       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6603       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6630       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6658       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6685       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6712       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6740       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6767       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6795       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6822       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6849       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6877       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6904       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6932       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6959       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.6986       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7014       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7041       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7068       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7096       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7123       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7151       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7178       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7205       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7233       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7260       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7288       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7315       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7342       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7370       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7397       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7425       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7452       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7479       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7507       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7534       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7562       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7589       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7616       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7644       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7671       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7699       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7726       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7753       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7781       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7808       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7836       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7863       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7890       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7918       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7945       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.7973       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8000       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8027       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8055       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8082       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8110       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8137       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8164       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8192       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8219       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8247       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8274       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8301       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8329       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8356       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8384       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8411       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8438       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8466       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8493       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8521       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8548       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8575       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8603       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8630       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8658       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8685       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8712       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8740       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8767       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8795       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8822       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8849       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8877       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8904       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8932       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8959       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.8986       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9014       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9041       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9068       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9096       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9123       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9151       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9178       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9205       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9233       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9260       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9288       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9315       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9342       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9370       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9397       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9425       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9452       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9479       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9507       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9534       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9562       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9589       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9616       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9644       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9671       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9699       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9726       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9753       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9781       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9808       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9836       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9863       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9890       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9918       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9945       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2023.9973       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0000       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0027       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0055       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0082       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0110       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0137       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0164       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0192       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0219       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0247       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0274       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0301       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0329       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0356       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0384       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0411       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0438       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0466       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0493       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0521       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0548       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0575       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0603       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0630       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0658       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0685       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0712       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0740       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0767       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0795       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0822       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0849       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0877       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0904       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0932       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0959       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.0986       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1014       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1041       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1068       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1096       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1123       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1151       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1178       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1205       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1233       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1260       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1288       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1315       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1342       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1370       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1397       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1425       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1452       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1479       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1507       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1534       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1562       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1589       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1616       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1644       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1671       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1699       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1726       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1753       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1781       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1808       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1836       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1863       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1890       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1918       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1945       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.1973       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2000       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2027       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2055       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2082       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2110       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2137       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2164       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2192       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2219       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2247       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2274       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2301       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2329       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2356       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2384       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2411       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2438       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2466       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2493       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2521       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2548       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2575       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2603       1.851136 -3.8539 7.556173 -6.879428 10.5817
## 2024.2630       1.851136 -3.8539 7.556173 -6.879428 10.5817

print(average_model$mean)

## Time Series:
## Start = c(2023, 90) 
## End = c(2024, 97) 
## Frequency = 365 
##   [1] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
##   [9] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
##  [17] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
##  [25] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
##  [33] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
##  [41] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
##  [49] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
##  [57] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
##  [65] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
##  [73] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
##  [81] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
##  [89] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
##  [97] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [105] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [113] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [121] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [129] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [137] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [145] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [153] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [161] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [169] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [177] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [185] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [193] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [201] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [209] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [217] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [225] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [233] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [241] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [249] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [257] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [265] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [273] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [281] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [289] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [297] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [305] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [313] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [321] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [329] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [337] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [345] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [353] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [361] 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136 1.851136
## [369] 1.851136 1.851136 1.851136 1.851136 1.851136

print(train_acc_ave)

##                         ME     RMSE      MAE  MPE MAPE    MASE      ACF1
## Training set -4.341224e-14 4.443266 2.305132 -Inf  Inf 0.73371 0.7949995

print(test_acc_ave)

##                         ME     RMSE      MAE  MPE MAPE      MASE       ACF1
## Training set -4.341224e-14 4.443266 2.305132 -Inf  Inf 0.7337100 0.79499952
## Test set     -1.773388e+00 1.799460 1.776581 -Inf  Inf 0.5654755 0.05005751
##              Theil's U
## Training set        NA
## Test set             0

Regular TS-naive method

naive_model <- naive(train, h = length(test))
print(naive_model$mean)

## Time Series:
## Start = c(2023, 90) 
## End = c(2024, 97) 
## Frequency = 365 
##   [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##  [38] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##  [75] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [112] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [149] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [186] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [223] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [260] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [297] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [334] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [371] 0 0 0

train_acc_nai <- last(train)
test_acc_nai <- accuracy(naive_model, x = regular_ts)

ts_plot <- autoplot(train) +
  autolayer(average_model, PI = F, size = 1.1, series = 'Average Model') +
  autolayer(naive_model, PI = F, size = 1.1, series = 'Naive Model') +
  autolayer(test, series = 'Test Data')

Regular TS-seasonal naive method

seasonal_naive_model <- snaive(train, h = length(test))
print(seasonal_naive_model)

##           Point Forecast      Lo 80     Hi 80      Lo 95    Hi 95
## 2023.2438              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.2466              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.2493              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.2521              2  -6.084364 10.084364 -10.363967 14.36397
## 2023.2548              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.2575              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.2603              2  -6.084364 10.084364 -10.363967 14.36397
## 2023.2630              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.2658              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.2685              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.2712              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.2740              2  -6.084364 10.084364 -10.363967 14.36397
## 2023.2767              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.2795              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.2822              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.2849              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.2877              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.2904              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.2932              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.2959              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.2986              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3014              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3041              2  -6.084364 10.084364 -10.363967 14.36397
## 2023.3068              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3096              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3123              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3151              2  -6.084364 10.084364 -10.363967 14.36397
## 2023.3178              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3205              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.3233              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3260              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3288              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3315              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3342              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3370              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3397              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3425              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3452              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3479              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3507              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3534              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3562              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3589              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3616              2  -6.084364 10.084364 -10.363967 14.36397
## 2023.3644              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3671              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.3699              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3726              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.3753              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3781              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3808              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3836              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3863              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3890              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3918              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.3945              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.3973              6  -2.084364 14.084364  -6.363967 18.36397
## 2023.4000              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4027              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4055              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4082              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4110              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4137              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4164              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.4192              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4219              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4247              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.4274              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4301              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.4329              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4356              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.4384              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4411              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4438              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4466              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4493              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4521              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4548              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4575              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.4603              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4630              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4658              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4685              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4712              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.4740              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4767              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4795              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4822              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4849              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4877              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4904              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.4932              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4959              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.4986              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5014              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5041              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.5068              2  -6.084364 10.084364 -10.363967 14.36397
## 2023.5096              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5123              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5151              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5178              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5205              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5233              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5260              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5288              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5315              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.5342              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5370              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.5397              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5425              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.5452              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5479              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5507              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5534              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5562              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5589              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5616              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5644              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5671              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5699              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5726              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5753              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5781              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5808              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.5836              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5863              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5890              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5918              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5945              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.5973              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6000              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6027              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6055              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6082              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6110              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6137              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6164              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6192              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6219              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6247              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6274              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6301              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6329              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6356              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6384              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6411              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.6438              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6466              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6493              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6521              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.6548              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6575              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6603              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6630              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6658              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6685              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6712              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6740              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.6767              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6795              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.6822              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6849              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.6877              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6904              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6932              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6959              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.6986              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.7014              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.7041              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7068              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7096              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7123              2  -6.084364 10.084364 -10.363967 14.36397
## 2023.7151              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.7178              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7205              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7233              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.7260              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7288              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7315              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7342              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7370              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7397              2  -6.084364 10.084364 -10.363967 14.36397
## 2023.7425              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.7452              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7479              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.7507              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7534              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7562              2  -6.084364 10.084364 -10.363967 14.36397
## 2023.7589              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7616              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7644              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7671              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7699              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7726              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7753              2  -6.084364 10.084364 -10.363967 14.36397
## 2023.7781              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7808              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7836              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7863              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.7890              5  -3.084364 13.084364  -7.363967 17.36397
## 2023.7918              2  -6.084364 10.084364 -10.363967 14.36397
## 2023.7945              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.7973              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.8000              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8027              2  -6.084364 10.084364 -10.363967 14.36397
## 2023.8055              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.8082              2  -6.084364 10.084364 -10.363967 14.36397
## 2023.8110              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.8137              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8164              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8192              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.8219              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8247              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8274              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.8301              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8329              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8356              1  -7.084364  9.084364 -11.363967 13.36397
## 2023.8384              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8411              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8438              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8466              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8493              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8521              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8548              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8575              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8603              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8630              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8658              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8685              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8712              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8740              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8767              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8795              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8822              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8849              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8877              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8904              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8932              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8959              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.8986              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9014              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9041              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9068              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9096              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9123              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9151              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9178              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9205              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9233              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9260              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9288              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9315              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9342              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9370              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9397              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9425              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9452              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9479              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9507              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9534              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9562              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9589              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9616              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9644              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9671              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9699              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9726              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9753              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9781              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9808              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9836              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9863              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9890              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9918              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9945              0  -8.084364  8.084364 -12.363967 12.36397
## 2023.9973              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0000              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0027              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0055              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0082              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0110              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0137              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0164              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0192              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0219              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0247              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0274              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0301              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0329              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0356              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0384              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0411              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0438              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0466              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0493              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0521              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0548              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0575              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0603              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0630              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0658              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0685              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0712              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0740              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0767              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0795              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0822              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0849              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0877              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0904              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0932              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0959              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.0986              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1014              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1041              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1068              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1096              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1123              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1151              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1178              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1205              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1233              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1260              1  -7.084364  9.084364 -11.363967 13.36397
## 2024.1288              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1315              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1342              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1370              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1397              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1425              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1452              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1479              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1507              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1534              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1562              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1589              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1616              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1644              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1671              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1699              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1726              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1753              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1781              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1808              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1836              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1863              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1890              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1918              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1945              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.1973              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.2000              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.2027              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.2055              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.2082              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.2110              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.2137              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.2164              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.2192              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.2219              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.2247              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.2274              1  -7.084364  9.084364 -11.363967 13.36397
## 2024.2301              1  -7.084364  9.084364 -11.363967 13.36397
## 2024.2329              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.2356              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.2384              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.2411              0  -8.084364  8.084364 -12.363967 12.36397
## 2024.2438              0 -11.433017 11.433017 -17.485290 17.48529
## 2024.2466              1 -10.433017 12.433017 -16.485290 18.48529
## 2024.2493              0 -11.433017 11.433017 -17.485290 17.48529
## 2024.2521              2  -9.433017 13.433017 -15.485290 19.48529
## 2024.2548              0 -11.433017 11.433017 -17.485290 17.48529
## 2024.2575              0 -11.433017 11.433017 -17.485290 17.48529
## 2024.2603              2  -9.433017 13.433017 -15.485290 19.48529
## 2024.2630              0 -11.433017 11.433017 -17.485290 17.48529

print(seasonal_naive_model$mean)

## Time Series:
## Start = c(2023, 90) 
## End = c(2024, 97) 
## Frequency = 365 
##   [1] 0 1 0 2 0 0 2 0 1 1 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 1 0 0 0 0 0 0 0 0
##  [38] 0 0 0 0 0 0 2 0 1 0 1 0 0 0 0 0 0 0 1 6 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0
##  [75] 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 2 0 0 0 0 0 0 0 0 1 0 1 0 1 0
## [112] 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
## [149] 0 1 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 2 1 0 0 1 0 0 0 0 0 2 1 0 1
## [186] 0 0 2 0 0 0 0 0 0 2 0 0 0 1 5 2 0 1 0 2 1 2 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0
## [223] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [260] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [297] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
## [334] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 2 0
## [371] 0 2 0

test_acc_snai <- accuracy(seasonal_naive_model, x = regular_ts)
print(test_acc_snai)

##                      ME      RMSE       MAE  MPE MAPE       MASE      ACF1
## Training set -2.2796117 6.3082624 3.1417476 -Inf  Inf 1.00000000 0.7674117
## Test set     -0.1474531 0.7304191 0.2975871 -Inf  Inf 0.09472026 0.1564688
##              Theil's U
## Training set        NA
## Test set             0

seasonal_ts_plot <- autoplot(train) +
  autolayer(seasonal_naive_model, PI = F, size = 1.1, series = 'Seasonal Naive Model') +
  autolayer(test, series = 'Test Data')

Regular TS-drift method

drift_model <- rwf(train, h = length(test), drift = TRUE)
text_file_name <- paste0(character_name, "_drift_model_output.txt")

print(drift_model)

##           Point Forecast      Lo 80     Hi 80       Lo 95      Hi 95
## 2023.2438   -0.001137656  -3.652418  3.650143   -5.585289   5.583014
## 2023.2466   -0.002275313  -5.168899  5.164348   -7.903944   7.899393
## 2023.2493   -0.003412969  -6.334799  6.327973   -9.686432   9.679606
## 2023.2521   -0.004550626  -7.319548  7.310447  -11.191874  11.182773
## 2023.2548   -0.005688282  -8.188734  8.177358  -12.520577  12.509200
## 2023.2575   -0.006825939  -8.975972  8.962320  -13.723952  13.710300
## 2023.2603   -0.007963595  -9.701221  9.685294  -14.832521  14.816594
## 2023.2630   -0.009101251 -10.377475 10.359273  -15.866161  15.847958
## 2023.2658   -0.010238908 -11.013758 10.993280  -16.838669  16.818191
## 2023.2685   -0.011376564 -11.616633 11.593880  -17.760084  17.737331
## 2023.2712   -0.012514221 -12.191053 12.166025  -18.637983  18.612954
## 2023.2740   -0.013651877 -12.740865 12.713562  -19.478245  19.450941
## 2023.2767   -0.014789534 -13.269125 13.239546  -20.285546  20.255967
## 2023.2795   -0.015927190 -13.778309 13.746455  -21.063674  21.031819
## 2023.2822   -0.017064846 -14.270457 14.236328  -21.815747  21.781618
## 2023.2849   -0.018202503 -14.747274 14.710869  -22.544373  22.507968
## 2023.2877   -0.019340159 -15.210199 15.171518  -23.251753  23.213073
## 2023.2904   -0.020477816 -15.660463 15.619507  -23.939770  23.898815
## 2023.2932   -0.021615472 -16.099127 16.055896  -24.610047  24.566816
## 2023.2959   -0.022753129 -16.527113 16.481607  -25.263994  25.218488
## 2023.2986   -0.023890785 -16.945231 16.897449  -25.902847  25.855066
## 2023.3014   -0.025028441 -17.354191 17.304135  -26.527696  26.477639
## 2023.3041   -0.026166098 -17.754627 17.702295  -27.139508  27.087175
## 2023.3068   -0.027303754 -18.147102 18.092494  -27.739143  27.684536
## 2023.3096   -0.028441411 -18.532120 18.475237  -28.327375  28.270493
## 2023.3123   -0.029579067 -18.910137 18.850978  -28.904900  28.845742
## 2023.3151   -0.030716724 -19.281563 19.220130  -29.472346  29.410912
## 2023.3178   -0.031854380 -19.646773 19.583064  -30.030284  29.966575
## 2023.3205   -0.032992036 -20.006106 19.940122  -30.579234  30.513249
## 2023.3233   -0.034129693 -20.359872 20.291613  -31.119670  31.051411
## 2023.3260   -0.035267349 -20.708357 20.637823  -31.652030  31.581495
## 2023.3288   -0.036405006 -21.051823 20.979013  -32.176713  32.103903
## 2023.3315   -0.037542662 -21.390510 21.315425  -32.694088  32.619003
## 2023.3342   -0.038680319 -21.724643 21.647282  -33.204498  33.127137
## 2023.3370   -0.039817975 -22.054427 21.974791  -33.708257  33.628621
## 2023.3397   -0.040955631 -22.380054 22.298143  -34.205659  34.123748
## 2023.3425   -0.042093288 -22.701704 22.617518  -34.696978  34.612791
## 2023.3452   -0.043230944 -23.019543 22.933081  -35.182468  35.096006
## 2023.3479   -0.044368601 -23.333725 23.244988  -35.662366  35.573629
## 2023.3507   -0.045506257 -23.644398 23.553385  -36.136896  36.045884
## 2023.3534   -0.046643914 -23.951696 23.858408  -36.606266  36.512978
## 2023.3562   -0.047781570 -24.255748 24.160185  -37.070672  36.975109
## 2023.3589   -0.048919226 -24.556675 24.458836  -37.530297  37.432458
## 2023.3616   -0.050056883 -24.854589 24.754475  -37.985315  37.885201
## 2023.3644   -0.051194539 -25.149598 25.047209  -38.435890  38.333501
## 2023.3671   -0.052332196 -25.441802 25.337138  -38.882176  38.777511
## 2023.3699   -0.053469852 -25.731297 25.624357  -39.324318  39.217378
## 2023.3726   -0.054607509 -26.018173 25.908958  -39.762455  39.653240
## 2023.3753   -0.055745165 -26.302516 26.191026  -40.196717  40.085227
## 2023.3781   -0.056882821 -26.584407 26.470641  -40.627229  40.513464
## 2023.3808   -0.058020478 -26.863922 26.747881  -41.054109  40.938068
## 2023.3836   -0.059158134 -27.141135 27.022819  -41.477468  41.359151
## 2023.3863   -0.060295791 -27.416116 27.295525  -41.897413  41.776821
## 2023.3890   -0.061433447 -27.688931 27.566064  -42.314045  42.191178
## 2023.3918   -0.062571104 -27.959644 27.834502  -42.727462  42.602320
## 2023.3945   -0.063708760 -28.228314 28.100897  -43.137756  43.010338
## 2023.3973   -0.064846416 -28.495000 28.365307  -43.545014  43.415321
## 2023.4000   -0.065984073 -28.759756 28.627788  -43.949322  43.817353
## 2023.4027   -0.067121729 -29.022636 28.888392  -44.350759  44.216515
## 2023.4055   -0.068259386 -29.283689 29.147170  -44.749403  44.612884
## 2023.4082   -0.069397042 -29.542964 29.404170  -45.145328  45.006534
## 2023.4110   -0.070534699 -29.800507 29.659438  -45.538604  45.397535
## 2023.4137   -0.071672355 -30.056363 29.913019  -45.929300  45.785955
## 2023.4164   -0.072810011 -30.310575 30.164955  -46.317481  46.171861
## 2023.4192   -0.073947668 -30.563183 30.415287  -46.703209  46.555313
## 2023.4219   -0.075085324 -30.814226 30.664055  -47.086544  46.936374
## 2023.4247   -0.076222981 -31.063743 30.911297  -47.467545  47.315099
## 2023.4274   -0.077360637 -31.311770 31.157049  -47.846268  47.691546
## 2023.4301   -0.078498294 -31.558342 31.401345  -48.222764  48.065768
## 2023.4329   -0.079635950 -31.803493 31.644221  -48.597088  48.437816
## 2023.4356   -0.080773606 -32.047255 31.885707  -48.969287  48.807740
## 2023.4384   -0.081911263 -32.289659 32.125837  -49.339411  49.175589
## 2023.4411   -0.083048919 -32.530737 32.364639  -49.707505  49.541407
## 2023.4438   -0.084186576 -32.770517 32.602143  -50.073615  49.905241
## 2023.4466   -0.085324232 -33.009027 32.838378  -50.437782  50.267134
## 2023.4493   -0.086461889 -33.246295 33.073371  -50.800050  50.627126
## 2023.4521   -0.087599545 -33.482347 33.307148  -51.160458  50.985259
## 2023.4548   -0.088737201 -33.717208 33.539734  -51.519045  51.341571
## 2023.4575   -0.089874858 -33.950904 33.771154  -51.875850  51.696100
## 2023.4603   -0.091012514 -34.183458 34.001433  -52.230908  52.048883
## 2023.4630   -0.092150171 -34.414892 34.230592  -52.584254  52.399954
## 2023.4658   -0.093287827 -34.645231 34.458655  -52.935924  52.749349
## 2023.4685   -0.094425484 -34.874494 34.685643  -53.285950  53.097099
## 2023.4712   -0.095563140 -35.102704 34.911577  -53.634365  53.443238
## 2023.4740   -0.096700796 -35.329880 35.136478  -53.981198  53.787797
## 2023.4767   -0.097838453 -35.556042 35.360366  -54.326482  54.130805
## 2023.4795   -0.098976109 -35.781210 35.583258  -54.670244  54.472292
## 2023.4822   -0.100113766 -36.005403 35.805175  -55.012514  54.812287
## 2023.4849   -0.101251422 -36.228637 36.026134  -55.353320  55.150817
## 2023.4877   -0.102389078 -36.450931 36.246153  -55.692687  55.487909
## 2023.4904   -0.103526735 -36.672302 36.465248  -56.030642  55.823589
## 2023.4932   -0.104664391 -36.892766 36.683437  -56.367211  56.157882
## 2023.4959   -0.105802048 -37.112340 36.900736  -56.702418  56.490814
## 2023.4986   -0.106939704 -37.331039 37.117160  -57.036287  56.822408
## 2023.5014   -0.108077361 -37.548878 37.332724  -57.368841  57.152687
## 2023.5041   -0.109215017 -37.765873 37.547443  -57.700104  57.481674
## 2023.5068   -0.110352673 -37.982038 37.761332  -58.030097  57.809391
## 2023.5096   -0.111490330 -38.197386 37.974405  -58.358841  58.135860
## 2023.5123   -0.112627986 -38.411932 38.186676  -58.686358  58.461102
## 2023.5151   -0.113765643 -38.625688 38.398157  -59.012668  58.785137
## 2023.5178   -0.114903299 -38.838668 38.608862  -59.337791  59.107985
## 2023.5205   -0.116040956 -39.050885 38.818803  -59.661747  59.429665
## 2023.5233   -0.117178612 -39.262351 39.027994  -59.984553  59.750196
## 2023.5260   -0.118316268 -39.473077 39.236445  -60.306229  60.069597
## 2023.5288   -0.119453925 -39.683077 39.444169  -60.626793  60.387885
## 2023.5315   -0.120591581 -39.892360 39.651177  -60.946262  60.705079
## 2023.5342   -0.121729238 -40.100938 39.857480  -61.264653  61.021195
## 2023.5370   -0.122866894 -40.308823 40.063089  -61.581983  61.336249
## 2023.5397   -0.124004551 -40.516025 40.268015  -61.898268  61.650259
## 2023.5425   -0.125142207 -40.722553 40.472269  -62.213525  61.963240
## 2023.5452   -0.126279863 -40.928420 40.675860  -62.527768  62.275208
## 2023.5479   -0.127417520 -41.133633 40.878798  -62.841012  62.586177
## 2023.5507   -0.128555176 -41.338204 41.081093  -63.153274  62.896163
## 2023.5534   -0.129692833 -41.542141 41.282755  -63.464566  63.205181
## 2023.5562   -0.130830489 -41.745453 41.483792  -63.774904  63.513243
## 2023.5589   -0.131968146 -41.948151 41.684215  -64.084301  63.820365
## 2023.5616   -0.133105802 -42.150242 41.884031  -64.392771  64.126559
## 2023.5644   -0.134243458 -42.351736 42.083249  -64.700326  64.431840
## 2023.5671   -0.135381115 -42.552640 42.281878  -65.006981  64.736219
## 2023.5699   -0.136518771 -42.752964 42.479926  -65.312747  65.039710
## 2023.5726   -0.137656428 -42.952714 42.677402  -65.617637  65.342324
## 2023.5753   -0.138794084 -43.151900 42.874312  -65.921663  65.644075
## 2023.5781   -0.139931741 -43.350529 43.070665  -66.224837  65.944974
## 2023.5808   -0.141069397 -43.548608 43.266469  -66.527171  66.245032
## 2023.5836   -0.142207053 -43.746145 43.461731  -66.828676  66.544262
## 2023.5863   -0.143344710 -43.943148 43.656458  -67.129363  66.842673
## 2023.5890   -0.144482366 -44.139622 43.850657  -67.429242  67.140278
## 2023.5918   -0.145620023 -44.335576 44.044336  -67.728326  67.437086
## 2023.5945   -0.146757679 -44.531017 44.237501  -68.026624  67.733109
## 2023.5973   -0.147895336 -44.725950 44.430159  -68.324146  68.028356
## 2023.6000   -0.149032992 -44.920383 44.622317  -68.620903  68.322838
## 2023.6027   -0.150170648 -45.114321 44.813980  -68.916905  68.616564
## 2023.6055   -0.151308305 -45.307772 45.005156  -69.212161  68.909544
## 2023.6082   -0.152445961 -45.500742 45.195850  -69.506680  69.201788
## 2023.6110   -0.153583618 -45.693236 45.386069  -69.800472  69.493305
## 2023.6137   -0.154721274 -45.885261 45.575818  -70.093546  69.784104
## 2023.6164   -0.155858931 -46.076822 45.765104  -70.385912  70.074194
## 2023.6192   -0.156996587 -46.267926 45.953932  -70.677577  70.363584
## 2023.6219   -0.158134243 -46.458577 46.142308  -70.968550  70.652282
## 2023.6247   -0.159271900 -46.648781 46.330237  -71.258841  70.940297
## 2023.6274   -0.160409556 -46.838544 46.517725  -71.548456  71.227637
## 2023.6301   -0.161547213 -47.027872 46.704777  -71.837405  71.514311
## 2023.6329   -0.162684869 -47.216768 46.891399  -72.125695  71.800326
## 2023.6356   -0.163822526 -47.405239 47.077594  -72.413335  72.085690
## 2023.6384   -0.164960182 -47.593290 47.263370  -72.700331  72.370411
## 2023.6411   -0.166097838 -47.780925 47.448729  -72.986692  72.654496
## 2023.6438   -0.167235495 -47.968149 47.633678  -73.272425  72.937954
## 2023.6466   -0.168373151 -48.154968 47.818221  -73.557537  73.220790
## 2023.6493   -0.169510808 -48.341385 48.002363  -73.842035  73.503013
## 2023.6521   -0.170648464 -48.527406 48.186109  -74.125927  73.784630
## 2023.6548   -0.171786121 -48.713034 48.369462  -74.409219  74.065646
## 2023.6575   -0.172923777 -48.898275 48.552427  -74.691918  74.346070
## 2023.6603   -0.174061433 -49.083133 48.735010  -74.974031  74.625908
## 2023.6630   -0.175199090 -49.267611 48.917213  -75.255565  74.905166
## 2023.6658   -0.176336746 -49.451715 49.099042  -75.536525  75.183852
## 2023.6685   -0.177474403 -49.635449 49.280500  -75.816919  75.461970
## 2023.6712   -0.178612059 -49.818816 49.461592  -76.096752  75.739528
## 2023.6740   -0.179749716 -50.001820 49.642321  -76.376031  76.016532
## 2023.6767   -0.180887372 -50.184466 49.822692  -76.654762  76.292988
## 2023.6795   -0.182025028 -50.366758 50.002708  -76.932951  76.568901
## 2023.6822   -0.183162685 -50.548699 50.182373  -77.210603  76.844277
## 2023.6849   -0.184300341 -50.730292 50.361692  -77.487724  77.119123
## 2023.6877   -0.185437998 -50.911543 50.540667  -77.764320  77.393444
## 2023.6904   -0.186575654 -51.092453 50.719302  -78.040397  77.667246
## 2023.6932   -0.187713311 -51.273028 50.897601  -78.315960  77.940533
## 2023.6959   -0.188850967 -51.453270 51.075568  -78.591014  78.213312
## 2023.6986   -0.189988623 -51.633183 51.253206  -78.865565  78.485588
## 2023.7014   -0.191126280 -51.812771 51.430518  -79.139618  78.757366
## 2023.7041   -0.192263936 -51.992036 51.607508  -79.413178  79.028650
## 2023.7068   -0.193401593 -52.170982 51.784179  -79.686251  79.299447
## 2023.7096   -0.194539249 -52.349612 51.960534  -79.958840  79.569761
## 2023.7123   -0.195676906 -52.527930 52.136576  -80.230951  79.839598
## 2023.7151   -0.196814562 -52.705939 52.312309  -80.502590  80.108961
## 2023.7178   -0.197952218 -52.883641 52.487736  -80.773760  80.377855
## 2023.7205   -0.199089875 -53.061040 52.662860  -81.044466  80.646286
## 2023.7233   -0.200227531 -53.238139 52.837684  -81.314714  80.914259
## 2023.7260   -0.201365188 -53.414941 53.012211  -81.584507  81.181776
## 2023.7288   -0.202502844 -53.591449 53.186443  -81.853850  81.448844
## 2023.7315   -0.203640501 -53.767665 53.360384  -82.122747  81.715466
## 2023.7342   -0.204778157 -53.943593 53.534037  -82.391203  81.981647
## 2023.7370   -0.205915813 -54.119235 53.707404  -82.659223  82.247391
## 2023.7397   -0.207053470 -54.294595 53.880488  -82.926809  82.512702
## 2023.7425   -0.208191126 -54.469674 54.053291  -83.193967  82.777585
## 2023.7452   -0.209328783 -54.644475 54.225818  -83.460701  83.042044
## 2023.7479   -0.210466439 -54.819002 54.398069  -83.727014  83.306082
## 2023.7507   -0.211604096 -54.993256 54.570048  -83.992912  83.569703
## 2023.7534   -0.212741752 -55.167241 54.741758  -84.258396  83.832913
## 2023.7562   -0.213879408 -55.340959 54.913200  -84.523472  84.095713
## 2023.7589   -0.215017065 -55.514412 55.084378  -84.788144  84.358109
## 2023.7616   -0.216154721 -55.687603 55.255294  -85.052414  84.620104
## 2023.7644   -0.217292378 -55.860534 55.425949  -85.316287  84.881702
## 2023.7671   -0.218430034 -56.033208 55.596348  -85.579767  85.142907
## 2023.7699   -0.219567691 -56.205627 55.766491  -85.842856  85.403721
## 2023.7726   -0.220705347 -56.377793 55.936382  -86.105560  85.664149
## 2023.7753   -0.221843003 -56.549709 56.106023  -86.367880  85.924194
## 2023.7781   -0.222980660 -56.721377 56.275416  -86.629821  86.183860
## 2023.7808   -0.224118316 -56.892799 56.444562  -86.891386  86.443150
## 2023.7836   -0.225255973 -57.063977 56.613465  -87.152579  86.702067
## 2023.7863   -0.226393629 -57.234914 56.782127  -87.413402  86.960615
## 2023.7890   -0.227531286 -57.405612 56.950549  -87.673859  87.218797
## 2023.7918   -0.228668942 -57.576072 57.118734  -87.933954  87.476616
## 2023.7945   -0.229806598 -57.746298 57.286685  -88.193689  87.734076
## 2023.7973   -0.230944255 -57.916290 57.454402  -88.453068  87.991179
## 2023.8000   -0.232081911 -58.086052 57.621888  -88.712093  88.247929
## 2023.8027   -0.233219568 -58.255584 57.789145  -88.970769  88.504329
## 2023.8055   -0.234357224 -58.424890 57.956175  -89.229097  88.760382
## 2023.8082   -0.235494881 -58.593970 58.122980  -89.487081  89.016091
## 2023.8110   -0.236632537 -58.762828 58.289563  -89.744724  89.271459
## 2023.8137   -0.237770193 -58.931464 58.455924  -90.002029  89.526488
## 2023.8164   -0.238907850 -59.099881 58.622065  -90.258998  89.781183
## 2023.8192   -0.240045506 -59.268081 58.787990  -90.515635  90.035544
## 2023.8219   -0.241183163 -59.436065 58.953699  -90.771942  90.289576
## 2023.8247   -0.242320819 -59.603835 59.119194  -91.027923  90.543281
## 2023.8274   -0.243458476 -59.771394 59.284477  -91.283579  90.796662
## 2023.8301   -0.244596132 -59.938742 59.449550  -91.538914  91.049722
## 2023.8329   -0.245733788 -60.105882 59.614414  -91.793930  91.302463
## 2023.8356   -0.246871445 -60.272815 59.779072  -92.048630  91.554887
## 2023.8384   -0.248009101 -60.439543 59.943525  -92.303017  91.806998
## 2023.8411   -0.249146758 -60.606068 60.107775  -92.557092  92.058799
## 2023.8438   -0.250284414 -60.772391 60.271822  -92.810859  92.310291
## 2023.8466   -0.251422071 -60.938515 60.435670  -93.064321  92.561477
## 2023.8493   -0.252559727 -61.104439 60.599320  -93.317479  92.812359
## 2023.8521   -0.253697383 -61.270168 60.762773  -93.570336  93.062941
## 2023.8548   -0.254835040 -61.435701 60.926031  -93.822895  93.313224
## 2023.8575   -0.255972696 -61.601040 61.089095  -94.075157  93.563212
## 2023.8603   -0.257110353 -61.766187 61.251967  -94.327126  93.812905
## 2023.8630   -0.258248009 -61.931144 61.414648  -94.578803  94.062307
## 2023.8658   -0.259385666 -62.095912 61.577141  -94.830192  94.311421
## 2023.8685   -0.260523322 -62.260492 61.739446  -95.081294  94.560247
## 2023.8712   -0.261660978 -62.424887 61.901565  -95.332111  94.808789
## 2023.8740   -0.262798635 -62.589097 62.063499  -95.582646  95.057048
## 2023.8767   -0.263936291 -62.753123 62.225251  -95.832901  95.305028
## 2023.8795   -0.265073948 -62.916968 62.386820  -96.082878  95.552730
## 2023.8822   -0.266211604 -63.080633 62.548210  -96.332579  95.800156
## 2023.8849   -0.267349261 -63.244119 62.709420  -96.582007  96.047308
## 2023.8877   -0.268486917 -63.407427 62.870453  -96.831163  96.294189
## 2023.8904   -0.269624573 -63.570559 63.031310  -97.080050  96.540801
## 2023.8932   -0.270762230 -63.733517 63.191992  -97.328669  96.787145
## 2023.8959   -0.271899886 -63.896301 63.352501  -97.577024  97.033224
## 2023.8986   -0.273037543 -64.058912 63.512837  -97.825115  97.279040
## 2023.9014   -0.274175199 -64.221353 63.673003  -98.072945  97.524594
## 2023.9041   -0.275312856 -64.383625 63.832999  -98.320515  97.769889
## 2023.9068   -0.276450512 -64.545728 63.992827  -98.567828  98.014927
## 2023.9096   -0.277588168 -64.707664 64.152488  -98.814886  98.259710
## 2023.9123   -0.278725825 -64.869435 64.311983  -99.061690  98.504239
## 2023.9151   -0.279863481 -65.031040 64.471313  -99.308243  98.748516
## 2023.9178   -0.281001138 -65.192483 64.630481  -99.554546  98.992544
## 2023.9205   -0.282138794 -65.353763 64.789486  -99.800601  99.236323
## 2023.9233   -0.283276451 -65.514883 64.948330 -100.046410  99.479857
## 2023.9260   -0.284414107 -65.675843 65.107015 -100.291974  99.723146
## 2023.9288   -0.285551763 -65.836644 65.265541 -100.537297  99.966193
## 2023.9315   -0.286689420 -65.997288 65.423909 -100.782378 100.208999
## 2023.9342   -0.287827076 -66.157776 65.582122 -101.027220 100.451566
## 2023.9370   -0.288964733 -66.318108 65.740179 -101.271826 100.693896
## 2023.9397   -0.290102389 -66.478287 65.898082 -101.516195 100.935991
## 2023.9425   -0.291240046 -66.638313 66.055833 -101.760331 101.177851
## 2023.9452   -0.292377702 -66.798186 66.213431 -102.004235 101.419480
## 2023.9479   -0.293515358 -66.957910 66.370879 -102.247908 101.660877
## 2023.9507   -0.294653015 -67.117483 66.528177 -102.491353 101.902047
## 2023.9534   -0.295790671 -67.276908 66.685327 -102.734570 102.142988
## 2023.9562   -0.296928328 -67.436185 66.842329 -102.977561 102.383705
## 2023.9589   -0.298065984 -67.595316 66.999184 -103.220329 102.624197
## 2023.9616   -0.299203641 -67.754302 67.155894 -103.462874 102.864466
## 2023.9644   -0.300341297 -67.913143 67.312460 -103.705198 103.104515
## 2023.9671   -0.301478953 -68.071840 67.468882 -103.947302 103.344345
## 2023.9699   -0.302616610 -68.230395 67.625162 -104.189189 103.583956
## 2023.9726   -0.303754266 -68.388809 67.781301 -104.430860 103.823351
## 2023.9753   -0.304891923 -68.547082 67.937298 -104.672316 104.062532
## 2023.9781   -0.306029579 -68.705216 68.093157 -104.913558 104.301499
## 2023.9808   -0.307167235 -68.863211 68.248877 -105.154589 104.540254
## 2023.9836   -0.308304892 -69.021069 68.404459 -105.395409 104.778799
## 2023.9863   -0.309442548 -69.178790 68.559905 -105.636020 105.017135
## 2023.9890   -0.310580205 -69.336375 68.715214 -105.876423 105.255263
## 2023.9918   -0.311717861 -69.493825 68.870389 -106.116621 105.493185
## 2023.9945   -0.312855518 -69.651142 69.025431 -106.356613 105.730902
## 2023.9973   -0.313993174 -69.808325 69.180339 -106.596402 105.968416
## 2024.0000   -0.315130830 -69.965377 69.335115 -106.835990 106.205728
## 2024.0027   -0.316268487 -70.122297 69.489760 -107.075376 106.442839
## 2024.0055   -0.317406143 -70.279087 69.644274 -107.314563 106.679751
## 2024.0082   -0.318543800 -70.435747 69.798659 -107.553552 106.916465
## 2024.0110   -0.319681456 -70.592279 69.952916 -107.792345 107.152982
## 2024.0137   -0.320819113 -70.748683 70.107045 -108.030942 107.389304
## 2024.0164   -0.321956769 -70.904960 70.261047 -108.269345 107.625431
## 2024.0192   -0.323094425 -71.061111 70.414922 -108.507555 107.861366
## 2024.0219   -0.324232082 -71.217137 70.568673 -108.745574 108.097110
## 2024.0247   -0.325369738 -71.373038 70.722299 -108.983402 108.332663
## 2024.0274   -0.326507395 -71.528816 70.875801 -109.221041 108.568027
## 2024.0301   -0.327645051 -71.684471 71.029181 -109.458493 108.803203
## 2024.0329   -0.328782708 -71.840004 71.182438 -109.695758 109.038192
## 2024.0356   -0.329920364 -71.995416 71.335575 -109.932837 109.272996
## 2024.0384   -0.331058020 -72.150707 71.488591 -110.169732 109.507616
## 2024.0411   -0.332195677 -72.305878 71.641487 -110.406445 109.742053
## 2024.0438   -0.333333333 -72.460931 71.794264 -110.642975 109.976308
## 2024.0466   -0.334470990 -72.615866 71.946924 -110.879325 110.210383
## 2024.0493   -0.335608646 -72.770683 72.099465 -111.115495 110.444277
## 2024.0521   -0.336746303 -72.925383 72.251891 -111.351486 110.677994
## 2024.0548   -0.337883959 -73.079968 72.404200 -111.587301 110.911533
## 2024.0575   -0.339021615 -73.234437 72.556394 -111.822939 111.144896
## 2024.0603   -0.340159272 -73.388792 72.708473 -112.058402 111.378084
## 2024.0630   -0.341296928 -73.543033 72.860439 -112.293691 111.611098
## 2024.0658   -0.342434585 -73.697161 73.012292 -112.528808 111.843939
## 2024.0685   -0.343572241 -73.851177 73.164033 -112.763753 112.076608
## 2024.0712   -0.344709898 -74.005081 73.315662 -112.998527 112.309107
## 2024.0740   -0.345847554 -74.158875 73.467179 -113.233131 112.541436
## 2024.0767   -0.346985210 -74.312558 73.618587 -113.467567 112.773596
## 2024.0795   -0.348122867 -74.466131 73.769885 -113.701835 113.005589
## 2024.0822   -0.349260523 -74.619596 73.921075 -113.935936 113.237415
## 2024.0849   -0.350398180 -74.772952 74.072156 -114.169872 113.469076
## 2024.0877   -0.351535836 -74.926201 74.223129 -114.403644 113.700572
## 2024.0904   -0.352673493 -75.079343 74.373996 -114.637252 113.931905
## 2024.0932   -0.353811149 -75.232379 74.524756 -114.870698 114.163076
## 2024.0959   -0.354948805 -75.385309 74.675411 -115.103982 114.394084
## 2024.0986   -0.356086462 -75.538134 74.825961 -115.337106 114.624933
## 2024.1014   -0.357224118 -75.690855 74.976406 -115.570070 114.855621
## 2024.1041   -0.358361775 -75.843472 75.126748 -115.802875 115.086152
## 2024.1068   -0.359499431 -75.995986 75.276987 -116.035523 115.316524
## 2024.1096   -0.360637088 -76.148397 75.427123 -116.268014 115.546740
## 2024.1123   -0.361774744 -76.300707 75.577158 -116.500350 115.776800
## 2024.1151   -0.362912400 -76.452916 75.727091 -116.732530 116.006705
## 2024.1178   -0.364050057 -76.605023 75.876923 -116.964557 116.236457
## 2024.1205   -0.365187713 -76.757031 76.026656 -117.196431 116.466055
## 2024.1233   -0.366325370 -76.908940 76.176289 -117.428152 116.695501
## 2024.1260   -0.367463026 -77.060749 76.325823 -117.659722 116.924796
## 2024.1288   -0.368600683 -77.212460 76.475259 -117.891143 117.153941
## 2024.1315   -0.369738339 -77.364074 76.624597 -118.122413 117.382937
## 2024.1342   -0.370875995 -77.515590 76.773838 -118.353535 117.611783
## 2024.1370   -0.372013652 -77.667010 76.922983 -118.584510 117.840482
## 2024.1397   -0.373151308 -77.818334 77.072031 -118.815337 118.069035
## 2024.1425   -0.374288965 -77.969562 77.220984 -119.046019 118.297441
## 2024.1452   -0.375426621 -78.120696 77.369843 -119.276555 118.525702
## 2024.1479   -0.376564278 -78.271735 77.518607 -119.506948 118.753819
## 2024.1507   -0.377701934 -78.422680 77.667277 -119.737196 118.981793
## 2024.1534   -0.378839590 -78.573533 77.815853 -119.967303 119.209623
## 2024.1562   -0.379977247 -78.724292 77.964337 -120.197267 119.437312
## 2024.1589   -0.381114903 -78.874959 78.112729 -120.427090 119.664860
## 2024.1616   -0.382252560 -79.025535 78.261029 -120.656773 119.892268
## 2024.1644   -0.383390216 -79.176019 78.409238 -120.886317 120.119537
## 2024.1671   -0.384527873 -79.326413 78.557357 -121.115722 120.346666
## 2024.1699   -0.385665529 -79.476716 78.705385 -121.344989 120.573658
## 2024.1726   -0.386803185 -79.626930 78.853324 -121.574120 120.800513
## 2024.1753   -0.387940842 -79.777055 79.001173 -121.803114 121.027232
## 2024.1781   -0.389078498 -79.927091 79.148934 -122.031972 121.253815
## 2024.1808   -0.390216155 -80.077040 79.296607 -122.260696 121.480263
## 2024.1836   -0.391353811 -80.226900 79.444193 -122.489285 121.706578
## 2024.1863   -0.392491468 -80.376674 79.591691 -122.717742 121.932759
## 2024.1890   -0.393629124 -80.526360 79.739102 -122.946066 122.158808
## 2024.1918   -0.394766780 -80.675961 79.886427 -123.174258 122.384725
## 2024.1945   -0.395904437 -80.825476 80.033667 -123.402319 122.610510
## 2024.1973   -0.397042093 -80.974906 80.180822 -123.630250 122.836166
## 2024.2000   -0.398179750 -81.124251 80.327891 -123.858051 123.061692
## 2024.2027   -0.399317406 -81.273511 80.474877 -124.085724 123.287089
## 2024.2055   -0.400455063 -81.422688 80.621778 -124.313268 123.512358
## 2024.2082   -0.401592719 -81.571782 80.768597 -124.540685 123.737499
## 2024.2110   -0.402730375 -81.720793 80.915332 -124.767974 123.962514
## 2024.2137   -0.403868032 -81.869721 81.061985 -124.995138 124.187402
## 2024.2164   -0.405005688 -82.018567 81.208556 -125.222177 124.412165
## 2024.2192   -0.406143345 -82.167332 81.355045 -125.449090 124.636804
## 2024.2219   -0.407281001 -82.316015 81.501453 -125.675880 124.861318
## 2024.2247   -0.408418658 -82.464618 81.647781 -125.902546 125.085709
## 2024.2274   -0.409556314 -82.613141 81.794028 -126.129090 125.309977
## 2024.2301   -0.410693970 -82.761584 81.940196 -126.355511 125.534123
## 2024.2329   -0.411831627 -82.909947 82.086284 -126.581811 125.758148
## 2024.2356   -0.412969283 -83.058232 82.232293 -126.807991 125.982052
## 2024.2384   -0.414106940 -83.206437 82.378224 -127.034050 126.205836
## 2024.2411   -0.415244596 -83.354565 82.524076 -127.259990 126.429500
## 2024.2438   -0.416382253 -83.502615 82.669851 -127.485810 126.653046
## 2024.2466   -0.417519909 -83.650588 82.815548 -127.711513 126.876473
## 2024.2493   -0.418657565 -83.798484 82.961169 -127.937098 127.099783
## 2024.2521   -0.419795222 -83.946304 83.106713 -128.162566 127.322976
## 2024.2548   -0.420932878 -84.094047 83.252181 -128.387918 127.546052
## 2024.2575   -0.422070535 -84.241715 83.397574 -128.613154 127.769013
## 2024.2603   -0.423208191 -84.389307 83.542891 -128.838275 127.991859
## 2024.2630   -0.424345848 -84.536825 83.688133 -129.063281 128.214590

print(drift_model$mean)

## Time Series:
## Start = c(2023, 90) 
## End = c(2024, 97) 
## Frequency = 365 
##   [1] -0.001137656 -0.002275313 -0.003412969 -0.004550626 -0.005688282
##   [6] -0.006825939 -0.007963595 -0.009101251 -0.010238908 -0.011376564
##  [11] -0.012514221 -0.013651877 -0.014789534 -0.015927190 -0.017064846
##  [16] -0.018202503 -0.019340159 -0.020477816 -0.021615472 -0.022753129
##  [21] -0.023890785 -0.025028441 -0.026166098 -0.027303754 -0.028441411
##  [26] -0.029579067 -0.030716724 -0.031854380 -0.032992036 -0.034129693
##  [31] -0.035267349 -0.036405006 -0.037542662 -0.038680319 -0.039817975
##  [36] -0.040955631 -0.042093288 -0.043230944 -0.044368601 -0.045506257
##  [41] -0.046643914 -0.047781570 -0.048919226 -0.050056883 -0.051194539
##  [46] -0.052332196 -0.053469852 -0.054607509 -0.055745165 -0.056882821
##  [51] -0.058020478 -0.059158134 -0.060295791 -0.061433447 -0.062571104
##  [56] -0.063708760 -0.064846416 -0.065984073 -0.067121729 -0.068259386
##  [61] -0.069397042 -0.070534699 -0.071672355 -0.072810011 -0.073947668
##  [66] -0.075085324 -0.076222981 -0.077360637 -0.078498294 -0.079635950
##  [71] -0.080773606 -0.081911263 -0.083048919 -0.084186576 -0.085324232
##  [76] -0.086461889 -0.087599545 -0.088737201 -0.089874858 -0.091012514
##  [81] -0.092150171 -0.093287827 -0.094425484 -0.095563140 -0.096700796
##  [86] -0.097838453 -0.098976109 -0.100113766 -0.101251422 -0.102389078
##  [91] -0.103526735 -0.104664391 -0.105802048 -0.106939704 -0.108077361
##  [96] -0.109215017 -0.110352673 -0.111490330 -0.112627986 -0.113765643
## [101] -0.114903299 -0.116040956 -0.117178612 -0.118316268 -0.119453925
## [106] -0.120591581 -0.121729238 -0.122866894 -0.124004551 -0.125142207
## [111] -0.126279863 -0.127417520 -0.128555176 -0.129692833 -0.130830489
## [116] -0.131968146 -0.133105802 -0.134243458 -0.135381115 -0.136518771
## [121] -0.137656428 -0.138794084 -0.139931741 -0.141069397 -0.142207053
## [126] -0.143344710 -0.144482366 -0.145620023 -0.146757679 -0.147895336
## [131] -0.149032992 -0.150170648 -0.151308305 -0.152445961 -0.153583618
## [136] -0.154721274 -0.155858931 -0.156996587 -0.158134243 -0.159271900
## [141] -0.160409556 -0.161547213 -0.162684869 -0.163822526 -0.164960182
## [146] -0.166097838 -0.167235495 -0.168373151 -0.169510808 -0.170648464
## [151] -0.171786121 -0.172923777 -0.174061433 -0.175199090 -0.176336746
## [156] -0.177474403 -0.178612059 -0.179749716 -0.180887372 -0.182025028
## [161] -0.183162685 -0.184300341 -0.185437998 -0.186575654 -0.187713311
## [166] -0.188850967 -0.189988623 -0.191126280 -0.192263936 -0.193401593
## [171] -0.194539249 -0.195676906 -0.196814562 -0.197952218 -0.199089875
## [176] -0.200227531 -0.201365188 -0.202502844 -0.203640501 -0.204778157
## [181] -0.205915813 -0.207053470 -0.208191126 -0.209328783 -0.210466439
## [186] -0.211604096 -0.212741752 -0.213879408 -0.215017065 -0.216154721
## [191] -0.217292378 -0.218430034 -0.219567691 -0.220705347 -0.221843003
## [196] -0.222980660 -0.224118316 -0.225255973 -0.226393629 -0.227531286
## [201] -0.228668942 -0.229806598 -0.230944255 -0.232081911 -0.233219568
## [206] -0.234357224 -0.235494881 -0.236632537 -0.237770193 -0.238907850
## [211] -0.240045506 -0.241183163 -0.242320819 -0.243458476 -0.244596132
## [216] -0.245733788 -0.246871445 -0.248009101 -0.249146758 -0.250284414
## [221] -0.251422071 -0.252559727 -0.253697383 -0.254835040 -0.255972696
## [226] -0.257110353 -0.258248009 -0.259385666 -0.260523322 -0.261660978
## [231] -0.262798635 -0.263936291 -0.265073948 -0.266211604 -0.267349261
## [236] -0.268486917 -0.269624573 -0.270762230 -0.271899886 -0.273037543
## [241] -0.274175199 -0.275312856 -0.276450512 -0.277588168 -0.278725825
## [246] -0.279863481 -0.281001138 -0.282138794 -0.283276451 -0.284414107
## [251] -0.285551763 -0.286689420 -0.287827076 -0.288964733 -0.290102389
## [256] -0.291240046 -0.292377702 -0.293515358 -0.294653015 -0.295790671
## [261] -0.296928328 -0.298065984 -0.299203641 -0.300341297 -0.301478953
## [266] -0.302616610 -0.303754266 -0.304891923 -0.306029579 -0.307167235
## [271] -0.308304892 -0.309442548 -0.310580205 -0.311717861 -0.312855518
## [276] -0.313993174 -0.315130830 -0.316268487 -0.317406143 -0.318543800
## [281] -0.319681456 -0.320819113 -0.321956769 -0.323094425 -0.324232082
## [286] -0.325369738 -0.326507395 -0.327645051 -0.328782708 -0.329920364
## [291] -0.331058020 -0.332195677 -0.333333333 -0.334470990 -0.335608646
## [296] -0.336746303 -0.337883959 -0.339021615 -0.340159272 -0.341296928
## [301] -0.342434585 -0.343572241 -0.344709898 -0.345847554 -0.346985210
## [306] -0.348122867 -0.349260523 -0.350398180 -0.351535836 -0.352673493
## [311] -0.353811149 -0.354948805 -0.356086462 -0.357224118 -0.358361775
## [316] -0.359499431 -0.360637088 -0.361774744 -0.362912400 -0.364050057
## [321] -0.365187713 -0.366325370 -0.367463026 -0.368600683 -0.369738339
## [326] -0.370875995 -0.372013652 -0.373151308 -0.374288965 -0.375426621
## [331] -0.376564278 -0.377701934 -0.378839590 -0.379977247 -0.381114903
## [336] -0.382252560 -0.383390216 -0.384527873 -0.385665529 -0.386803185
## [341] -0.387940842 -0.389078498 -0.390216155 -0.391353811 -0.392491468
## [346] -0.393629124 -0.394766780 -0.395904437 -0.397042093 -0.398179750
## [351] -0.399317406 -0.400455063 -0.401592719 -0.402730375 -0.403868032
## [356] -0.405005688 -0.406143345 -0.407281001 -0.408418658 -0.409556314
## [361] -0.410693970 -0.411831627 -0.412969283 -0.414106940 -0.415244596
## [366] -0.416382253 -0.417519909 -0.418657565 -0.419795222 -0.420932878
## [371] -0.422070535 -0.423208191 -0.424345848

test_acc_drift <- accuracy(drift_model, x = regular_ts)
print(test_acc_drift)

##                         ME      RMSE       MAE MPE MAPE      MASE       ACF1
## Training set -2.412775e-17 2.8458698 1.3873455 NaN  Inf 0.4415840 -0.2357073
## Test set      2.904897e-01 0.4478693 0.2904897 Inf  Inf 0.0924612  0.2374632
##              Theil's U
## Training set        NA
## Test set           NaN

drift_ts_plot <- autoplot(train) +
  autolayer(drift_model, PI = FALSE, size = 1.1, series = 'Drift Model') +
  autolayer(test, series = 'Test Data')

Regular TS-exponential smoothing models-simple exponential smoothing

ses_model <- ses(train, h = length(test))
ses_text_file_name <- paste0(character_name, "_ses_model_output.txt")

print(ses_model)

##           Point Forecast      Lo 80     Hi 80      Lo 95     Hi 95
## 2023.2438     0.03381961  -3.423620  3.491260  -5.253879  5.321518
## 2023.2466     0.03381961  -3.904820  3.972459  -5.989809  6.057449
## 2023.2493     0.03381961  -4.333315  4.400954  -6.645137  6.712776
## 2023.2521     0.03381961  -4.723370  4.791009  -7.241674  7.309313
## 2023.2548     0.03381961  -5.083781  5.151421  -7.792876  7.860515
## 2023.2575     0.03381961  -5.420429  5.488068  -8.307734  8.375373
## 2023.2603     0.03381961  -5.737473  5.805112  -8.792610  8.860250
## 2023.2630     0.03381961  -6.037984  6.105624  -9.252203  9.319842
## 2023.2658     0.03381961  -6.324308  6.391948  -9.690098  9.757737
## 2023.2685     0.03381961  -6.598282  6.665922 -10.109105 10.176744
## 2023.2712     0.03381961  -6.861379  6.929018 -10.511477 10.579116
## 2023.2740     0.03381961  -7.114799  7.182439 -10.899050 10.966689
## 2023.2767     0.03381961  -7.359538  7.427177 -11.273345 11.340985
## 2023.2795     0.03381961  -7.596431  7.664070 -11.635642 11.703281
## 2023.2822     0.03381961  -7.826188  7.893827 -11.987024 12.054663
## 2023.2849     0.03381961  -8.049416  8.117055 -12.328423 12.396062
## 2023.2877     0.03381961  -8.266644  8.334283 -12.660643 12.728283
## 2023.2904     0.03381961  -8.478329  8.545968 -12.984389 13.052028
## 2023.2932     0.03381961  -8.684877  8.752516 -13.300276 13.367915
## 2023.2959     0.03381961  -8.886643  8.954282 -13.608851 13.676490
## 2023.2986     0.03381961  -9.083945  9.151585 -13.910599 13.978238
## 2023.3014     0.03381961  -9.277068  9.344707 -14.205954 14.273593
## 2023.3041     0.03381961  -9.466265  9.533905 -14.495306 14.562946
## 2023.3068     0.03381961  -9.651768  9.719407 -14.779008 14.846647
## 2023.3096     0.03381961  -9.833783  9.901423 -15.057377 15.125016
## 2023.3123     0.03381961 -10.012502 10.080141 -15.330703 15.398342
## 2023.3151     0.03381961 -10.188096 10.255735 -15.599252 15.666891
## 2023.3178     0.03381961 -10.360725 10.428364 -15.863264 15.930903
## 2023.3205     0.03381961 -10.530533 10.598172 -16.122963 16.190602
## 2023.3233     0.03381961 -10.697654 10.765293 -16.378553 16.446192
## 2023.3260     0.03381961 -10.862212 10.929852 -16.630223 16.697862
## 2023.3288     0.03381961 -11.024322 11.091961 -16.878149 16.945788
## 2023.3315     0.03381961 -11.184090 11.251729 -17.122492 17.190131
## 2023.3342     0.03381961 -11.341613 11.409253 -17.363404 17.431043
## 2023.3370     0.03381961 -11.496985 11.564625 -17.601025 17.668664
## 2023.3397     0.03381961 -11.650291 11.717931 -17.835486 17.903125
## 2023.3425     0.03381961 -11.801612 11.869251 -18.066911 18.134550
## 2023.3452     0.03381961 -11.951022 12.018661 -18.295414 18.363053
## 2023.3479     0.03381961 -12.098592 12.166231 -18.521103 18.588742
## 2023.3507     0.03381961 -12.244389 12.312028 -18.744080 18.811719
## 2023.3534     0.03381961 -12.388474 12.456114 -18.964439 19.032079
## 2023.3562     0.03381961 -12.530908 12.598547 -19.182273 19.249912
## 2023.3589     0.03381961 -12.671745 12.739384 -19.397664 19.465303
## 2023.3616     0.03381961 -12.811037 12.878676 -19.610694 19.678333
## 2023.3644     0.03381961 -12.948836 13.016475 -19.821438 19.889077
## 2023.3671     0.03381961 -13.085187 13.152826 -20.029969 20.097608
## 2023.3699     0.03381961 -13.220135 13.287774 -20.236355 20.303994
## 2023.3726     0.03381961 -13.353723 13.421362 -20.440660 20.508299
## 2023.3753     0.03381961 -13.485991 13.553630 -20.642947 20.710586
## 2023.3781     0.03381961 -13.616978 13.684617 -20.843274 20.910913
## 2023.3808     0.03381961 -13.746720 13.814359 -21.041696 21.109336
## 2023.3836     0.03381961 -13.875251 13.942890 -21.238268 21.305908
## 2023.3863     0.03381961 -14.002606 14.070245 -21.433040 21.500680
## 2023.3890     0.03381961 -14.128815 14.196454 -21.626061 21.693700
## 2023.3918     0.03381961 -14.253910 14.321549 -21.817377 21.885016
## 2023.3945     0.03381961 -14.377919 14.445558 -22.007032 22.074671
## 2023.3973     0.03381961 -14.500869 14.568509 -22.195069 22.262708
## 2023.4000     0.03381961 -14.622789 14.690428 -22.381529 22.449168
## 2023.4027     0.03381961 -14.743702 14.811342 -22.566450 22.634089
## 2023.4055     0.03381961 -14.863635 14.931274 -22.749871 22.817510
## 2023.4082     0.03381961 -14.982609 15.050248 -22.931826 22.999466
## 2023.4110     0.03381961 -15.100648 15.168288 -23.112352 23.179991
## 2023.4137     0.03381961 -15.217774 15.285413 -23.291480 23.359119
## 2023.4164     0.03381961 -15.334007 15.401646 -23.469243 23.536882
## 2023.4192     0.03381961 -15.449367 15.517007 -23.645672 23.713311
## 2023.4219     0.03381961 -15.563875 15.631514 -23.820795 23.888435
## 2023.4247     0.03381961 -15.677548 15.745187 -23.994643 24.062282
## 2023.4274     0.03381961 -15.790404 15.858043 -24.167242 24.234881
## 2023.4301     0.03381961 -15.902461 15.970100 -24.338618 24.406257
## 2023.4329     0.03381961 -16.013735 16.081375 -24.508798 24.576437
## 2023.4356     0.03381961 -16.124244 16.191883 -24.677806 24.745445
## 2023.4384     0.03381961 -16.234001 16.301640 -24.845665 24.913305
## 2023.4411     0.03381961 -16.343023 16.410662 -25.012400 25.080039
## 2023.4438     0.03381961 -16.451324 16.518963 -25.178032 25.245672
## 2023.4466     0.03381961 -16.558918 16.626558 -25.342583 25.410223
## 2023.4493     0.03381961 -16.665819 16.733459 -25.506074 25.573714
## 2023.4521     0.03381961 -16.772040 16.839680 -25.668525 25.736165
## 2023.4548     0.03381961 -16.877594 16.945233 -25.829956 25.897595
## 2023.4575     0.03381961 -16.982493 17.050133 -25.990385 26.058024
## 2023.4603     0.03381961 -17.086750 17.154389 -26.149832 26.217471
## 2023.4630     0.03381961 -17.190375 17.258014 -26.308313 26.375952
## 2023.4658     0.03381961 -17.293381 17.361020 -26.465846 26.533486
## 2023.4685     0.03381961 -17.395777 17.463417 -26.622449 26.690088
## 2023.4712     0.03381961 -17.497576 17.565216 -26.778137 26.845776
## 2023.4740     0.03381961 -17.598787 17.666427 -26.932926 27.000565
## 2023.4767     0.03381961 -17.699421 17.767060 -27.086831 27.154470
## 2023.4795     0.03381961 -17.799486 17.867126 -27.239868 27.307508
## 2023.4822     0.03381961 -17.898994 17.966633 -27.392052 27.459691
## 2023.4849     0.03381961 -17.997952 18.065591 -27.543395 27.611034
## 2023.4877     0.03381961 -18.096370 18.164009 -27.693912 27.761551
## 2023.4904     0.03381961 -18.194256 18.261896 -27.843617 27.911256
## 2023.4932     0.03381961 -18.291620 18.359259 -27.992522 28.060161
## 2023.4959     0.03381961 -18.388469 18.456109 -28.140640 28.208279
## 2023.4986     0.03381961 -18.484812 18.552451 -28.287983 28.355623
## 2023.5014     0.03381961 -18.580656 18.648295 -28.434564 28.502203
## 2023.5041     0.03381961 -18.676009 18.743648 -28.580394 28.648033
## 2023.5068     0.03381961 -18.770879 18.838518 -28.725485 28.793124
## 2023.5096     0.03381961 -18.865272 18.932911 -28.869847 28.937486
## 2023.5123     0.03381961 -18.959196 19.026835 -29.013492 29.081131
## 2023.5151     0.03381961 -19.052658 19.120298 -29.156429 29.224069
## 2023.5178     0.03381961 -19.145665 19.213304 -29.298671 29.366310
## 2023.5205     0.03381961 -19.238223 19.305862 -29.440226 29.507865
## 2023.5233     0.03381961 -19.330338 19.397977 -29.581104 29.648743
## 2023.5260     0.03381961 -19.422017 19.489656 -29.721315 29.788954
## 2023.5288     0.03381961 -19.513267 19.580906 -29.860869 29.928508
## 2023.5315     0.03381961 -19.604092 19.671731 -29.999774 30.067413
## 2023.5342     0.03381961 -19.694499 19.762138 -30.138040 30.205679
## 2023.5370     0.03381961 -19.784494 19.852133 -30.275675 30.343314
## 2023.5397     0.03381961 -19.874081 19.941721 -30.412688 30.480327
## 2023.5425     0.03381961 -19.963268 20.030907 -30.549087 30.616726
## 2023.5452     0.03381961 -20.052059 20.119698 -30.684880 30.752519
## 2023.5479     0.03381961 -20.140458 20.208097 -30.820076 30.887715
## 2023.5507     0.03381961 -20.228472 20.296112 -30.954682 31.022321
## 2023.5534     0.03381961 -20.316106 20.383745 -31.088706 31.156345
## 2023.5562     0.03381961 -20.403363 20.471003 -31.222155 31.289794
## 2023.5589     0.03381961 -20.490250 20.557889 -31.355036 31.422676
## 2023.5616     0.03381961 -20.576770 20.644410 -31.487358 31.554997
## 2023.5644     0.03381961 -20.662929 20.730568 -31.619126 31.686765
## 2023.5671     0.03381961 -20.748731 20.816370 -31.750348 31.817988
## 2023.5699     0.03381961 -20.834179 20.901819 -31.881031 31.948670
## 2023.5726     0.03381961 -20.919280 20.986919 -32.011181 32.078820
## 2023.5753     0.03381961 -21.004036 21.071675 -32.140804 32.208443
## 2023.5781     0.03381961 -21.088452 21.156091 -32.269907 32.337546
## 2023.5808     0.03381961 -21.172532 21.240171 -32.398496 32.466135
## 2023.5836     0.03381961 -21.256280 21.323919 -32.526577 32.594217
## 2023.5863     0.03381961 -21.339699 21.407339 -32.654157 32.721796
## 2023.5890     0.03381961 -21.422795 21.490434 -32.781240 32.848879
## 2023.5918     0.03381961 -21.505570 21.573209 -32.907833 32.975473
## 2023.5945     0.03381961 -21.588028 21.655667 -33.033942 33.101581
## 2023.5973     0.03381961 -21.670172 21.737811 -33.159571 33.227211
## 2023.6000     0.03381961 -21.752007 21.819646 -33.284727 33.352366
## 2023.6027     0.03381961 -21.833536 21.901175 -33.409415 33.477054
## 2023.6055     0.03381961 -21.914762 21.982401 -33.533639 33.601278
## 2023.6082     0.03381961 -21.995688 22.063327 -33.657405 33.725044
## 2023.6110     0.03381961 -22.076318 22.143957 -33.780718 33.848357
## 2023.6137     0.03381961 -22.156655 22.224295 -33.903583 33.971223
## 2023.6164     0.03381961 -22.236703 22.304342 -34.026005 34.093645
## 2023.6192     0.03381961 -22.316464 22.384103 -34.147989 34.215628
## 2023.6219     0.03381961 -22.395941 22.463580 -34.269539 34.337178
## 2023.6247     0.03381961 -22.475137 22.542776 -34.390659 34.458298
## 2023.6274     0.03381961 -22.554056 22.621695 -34.511355 34.578994
## 2023.6301     0.03381961 -22.632700 22.700339 -34.631631 34.699270
## 2023.6329     0.03381961 -22.711072 22.778711 -34.751490 34.819130
## 2023.6356     0.03381961 -22.789175 22.856814 -34.870939 34.938578
## 2023.6384     0.03381961 -22.867012 22.934651 -34.989979 35.057619
## 2023.6411     0.03381961 -22.944585 23.012224 -35.108617 35.176256
## 2023.6438     0.03381961 -23.021896 23.089536 -35.226855 35.294495
## 2023.6466     0.03381961 -23.098950 23.166589 -35.344699 35.412338
## 2023.6493     0.03381961 -23.175748 23.243387 -35.462151 35.529790
## 2023.6521     0.03381961 -23.252292 23.319932 -35.579215 35.646855
## 2023.6548     0.03381961 -23.328586 23.396225 -35.695896 35.763536
## 2023.6575     0.03381961 -23.404631 23.472271 -35.812198 35.879837
## 2023.6603     0.03381961 -23.480431 23.548070 -35.928123 35.995762
## 2023.6630     0.03381961 -23.555987 23.623626 -36.043676 36.111315
## 2023.6658     0.03381961 -23.631301 23.698940 -36.158859 36.226499
## 2023.6685     0.03381961 -23.706377 23.774016 -36.273678 36.341317
## 2023.6712     0.03381961 -23.781216 23.848855 -36.388134 36.455773
## 2023.6740     0.03381961 -23.855821 23.923460 -36.502232 36.569871
## 2023.6767     0.03381961 -23.930193 23.997832 -36.615975 36.683614
## 2023.6795     0.03381961 -24.004335 24.071974 -36.729366 36.797005
## 2023.6822     0.03381961 -24.078249 24.145889 -36.842408 36.910047
## 2023.6849     0.03381961 -24.151938 24.219577 -36.955104 37.022743
## 2023.6877     0.03381961 -24.225402 24.293041 -37.067458 37.135098
## 2023.6904     0.03381961 -24.298645 24.366284 -37.179474 37.247113
## 2023.6932     0.03381961 -24.371668 24.439307 -37.291152 37.358792
## 2023.6959     0.03381961 -24.444473 24.512112 -37.402498 37.470137
## 2023.6986     0.03381961 -24.517062 24.584701 -37.513514 37.581153
## 2023.7014     0.03381961 -24.589437 24.657076 -37.624202 37.691841
## 2023.7041     0.03381961 -24.661600 24.729240 -37.734566 37.802205
## 2023.7068     0.03381961 -24.733553 24.801192 -37.844608 37.912248
## 2023.7096     0.03381961 -24.805298 24.872937 -37.954332 38.021971
## 2023.7123     0.03381961 -24.876835 24.944475 -38.063739 38.131379
## 2023.7151     0.03381961 -24.948168 25.015807 -38.172834 38.240473
## 2023.7178     0.03381961 -25.019298 25.086937 -38.281617 38.349257
## 2023.7205     0.03381961 -25.090226 25.157866 -38.390093 38.457732
## 2023.7233     0.03381961 -25.160955 25.228594 -38.498263 38.565903
## 2023.7260     0.03381961 -25.231486 25.299125 -38.606131 38.673770
## 2023.7288     0.03381961 -25.301820 25.369460 -38.713698 38.781337
## 2023.7315     0.03381961 -25.371960 25.439599 -38.820967 38.888607
## 2023.7342     0.03381961 -25.441907 25.509546 -38.927941 38.995581
## 2023.7370     0.03381961 -25.511662 25.579301 -39.034623 39.102262
## 2023.7397     0.03381961 -25.581227 25.648866 -39.141013 39.208653
## 2023.7425     0.03381961 -25.650603 25.718243 -39.247116 39.314755
## 2023.7452     0.03381961 -25.719793 25.787433 -39.352932 39.420572
## 2023.7479     0.03381961 -25.788798 25.856437 -39.458466 39.526105
## 2023.7507     0.03381961 -25.857618 25.925257 -39.563717 39.631357
## 2023.7534     0.03381961 -25.926256 25.993895 -39.668690 39.736330
## 2023.7562     0.03381961 -25.994713 26.062353 -39.773386 39.841026
## 2023.7589     0.03381961 -26.062991 26.130630 -39.877808 39.945447
## 2023.7616     0.03381961 -26.131090 26.198729 -39.981957 40.049596
## 2023.7644     0.03381961 -26.199013 26.266652 -40.085835 40.153474
## 2023.7671     0.03381961 -26.266760 26.334399 -40.189445 40.257085
## 2023.7699     0.03381961 -26.334333 26.401972 -40.292790 40.360429
## 2023.7726     0.03381961 -26.401733 26.469372 -40.395869 40.463509
## 2023.7753     0.03381961 -26.468962 26.536601 -40.498687 40.566326
## 2023.7781     0.03381961 -26.536021 26.603660 -40.601245 40.668884
## 2023.7808     0.03381961 -26.602911 26.670550 -40.703544 40.771184
## 2023.7836     0.03381961 -26.669633 26.737273 -40.805587 40.873227
## 2023.7863     0.03381961 -26.736189 26.803829 -40.907376 40.975016
## 2023.7890     0.03381961 -26.802581 26.870220 -41.008913 41.076552
## 2023.7918     0.03381961 -26.868808 26.936447 -41.110199 41.177838
## 2023.7945     0.03381961 -26.934872 27.002512 -41.211236 41.278875
## 2023.7973     0.03381961 -27.000776 27.068415 -41.312026 41.379665
## 2023.8000     0.03381961 -27.066518 27.134158 -41.412571 41.480210
## 2023.8027     0.03381961 -27.132102 27.199741 -41.512873 41.580512
## 2023.8055     0.03381961 -27.197528 27.265167 -41.612933 41.680572
## 2023.8082     0.03381961 -27.262797 27.330436 -41.712753 41.780392
## 2023.8110     0.03381961 -27.327910 27.395550 -41.812335 41.879975
## 2023.8137     0.03381961 -27.392869 27.460508 -41.911681 41.979321
## 2023.8164     0.03381961 -27.457674 27.525314 -42.010792 42.078432
## 2023.8192     0.03381961 -27.522327 27.589967 -42.109670 42.177310
## 2023.8219     0.03381961 -27.586829 27.654468 -42.208317 42.275956
## 2023.8247     0.03381961 -27.651180 27.718819 -42.306734 42.374373
## 2023.8274     0.03381961 -27.715382 27.783021 -42.404922 42.472561
## 2023.8301     0.03381961 -27.779436 27.847075 -42.502884 42.570523
## 2023.8329     0.03381961 -27.843343 27.910982 -42.600621 42.668260
## 2023.8356     0.03381961 -27.907103 27.974742 -42.698134 42.765773
## 2023.8384     0.03381961 -27.970718 28.038358 -42.795425 42.863064
## 2023.8411     0.03381961 -28.034189 28.101829 -42.892496 42.960135
## 2023.8438     0.03381961 -28.097517 28.165157 -42.989348 43.056987
## 2023.8466     0.03381961 -28.160703 28.228342 -43.085982 43.153621
## 2023.8493     0.03381961 -28.223747 28.291387 -43.182400 43.250039
## 2023.8521     0.03381961 -28.286652 28.354291 -43.278603 43.346243
## 2023.8548     0.03381961 -28.349416 28.417055 -43.374594 43.442233
## 2023.8575     0.03381961 -28.412042 28.479682 -43.470372 43.538011
## 2023.8603     0.03381961 -28.474531 28.542170 -43.565940 43.633579
## 2023.8630     0.03381961 -28.536883 28.604522 -43.661299 43.728938
## 2023.8658     0.03381961 -28.599099 28.666738 -43.756450 43.824090
## 2023.8685     0.03381961 -28.661180 28.728819 -43.851395 43.919035
## 2023.8712     0.03381961 -28.723127 28.790767 -43.946135 44.013775
## 2023.8740     0.03381961 -28.784941 28.852581 -44.040672 44.108311
## 2023.8767     0.03381961 -28.846623 28.914262 -44.135006 44.202645
## 2023.8795     0.03381961 -28.908173 28.975813 -44.229139 44.296778
## 2023.8822     0.03381961 -28.969593 29.037232 -44.323072 44.390711
## 2023.8849     0.03381961 -29.030883 29.098522 -44.416807 44.484446
## 2023.8877     0.03381961 -29.092044 29.159683 -44.510345 44.577984
## 2023.8904     0.03381961 -29.153077 29.220716 -44.603686 44.671325
## 2023.8932     0.03381961 -29.213982 29.281621 -44.696833 44.764472
## 2023.8959     0.03381961 -29.274761 29.342400 -44.789786 44.857425
## 2023.8986     0.03381961 -29.335414 29.403053 -44.882547 44.950186
## 2023.9014     0.03381961 -29.395942 29.463581 -44.975116 45.042756
## 2023.9041     0.03381961 -29.456346 29.523985 -45.067496 45.135135
## 2023.9068     0.03381961 -29.516626 29.584265 -45.159687 45.227326
## 2023.9096     0.03381961 -29.576784 29.644423 -45.251690 45.319329
## 2023.9123     0.03381961 -29.636819 29.704458 -45.343507 45.411146
## 2023.9151     0.03381961 -29.696734 29.764373 -45.435138 45.502777
## 2023.9178     0.03381961 -29.756527 29.824167 -45.526585 45.594224
## 2023.9205     0.03381961 -29.816202 29.883841 -45.617848 45.685488
## 2023.9233     0.03381961 -29.875757 29.943396 -45.708930 45.776569
## 2023.9260     0.03381961 -29.935193 30.002833 -45.799831 45.867470
## 2023.9288     0.03381961 -29.994513 30.062152 -45.890551 45.958191
## 2023.9315     0.03381961 -30.053715 30.121354 -45.981093 46.048732
## 2023.9342     0.03381961 -30.112801 30.180440 -46.071457 46.139096
## 2023.9370     0.03381961 -30.171771 30.239410 -46.161644 46.229284
## 2023.9397     0.03381961 -30.230626 30.298265 -46.251656 46.319295
## 2023.9425     0.03381961 -30.289367 30.357007 -46.341493 46.409132
## 2023.9452     0.03381961 -30.347995 30.415634 -46.431156 46.498795
## 2023.9479     0.03381961 -30.406510 30.474149 -46.520646 46.588286
## 2023.9507     0.03381961 -30.464912 30.532551 -46.609965 46.677604
## 2023.9534     0.03381961 -30.523203 30.590842 -46.699113 46.766753
## 2023.9562     0.03381961 -30.581383 30.649022 -46.788092 46.855731
## 2023.9589     0.03381961 -30.639452 30.707091 -46.876901 46.944540
## 2023.9616     0.03381961 -30.697412 30.765051 -46.965543 47.033182
## 2023.9644     0.03381961 -30.755262 30.822902 -47.054018 47.121657
## 2023.9671     0.03381961 -30.813004 30.880644 -47.142327 47.209966
## 2023.9699     0.03381961 -30.870639 30.938278 -47.230471 47.298110
## 2023.9726     0.03381961 -30.928166 30.995805 -47.318450 47.386090
## 2023.9753     0.03381961 -30.985586 31.053225 -47.406267 47.473906
## 2023.9781     0.03381961 -31.042900 31.110539 -47.493922 47.561561
## 2023.9808     0.03381961 -31.100109 31.167748 -47.581415 47.649054
## 2023.9836     0.03381961 -31.157212 31.224852 -47.668747 47.736387
## 2023.9863     0.03381961 -31.214212 31.281851 -47.755920 47.823560
## 2023.9890     0.03381961 -31.271107 31.338747 -47.842935 47.910574
## 2023.9918     0.03381961 -31.327900 31.395539 -47.929791 47.997430
## 2023.9945     0.03381961 -31.384589 31.452229 -48.016491 48.084130
## 2023.9973     0.03381961 -31.441177 31.508816 -48.103034 48.170673
## 2024.0000     0.03381961 -31.497663 31.565302 -48.189422 48.257061
## 2024.0027     0.03381961 -31.554048 31.621687 -48.275655 48.343294
## 2024.0055     0.03381961 -31.610333 31.677972 -48.361735 48.429374
## 2024.0082     0.03381961 -31.666517 31.734157 -48.447662 48.515301
## 2024.0110     0.03381961 -31.722603 31.790242 -48.533437 48.601076
## 2024.0137     0.03381961 -31.778589 31.846228 -48.619061 48.686700
## 2024.0164     0.03381961 -31.834477 31.902116 -48.704534 48.772173
## 2024.0192     0.03381961 -31.890267 31.957906 -48.789858 48.857497
## 2024.0219     0.03381961 -31.945960 32.013599 -48.875033 48.942672
## 2024.0247     0.03381961 -32.001556 32.069195 -48.960059 49.027699
## 2024.0274     0.03381961 -32.057056 32.124695 -49.044939 49.112578
## 2024.0301     0.03381961 -32.112460 32.180099 -49.129672 49.197311
## 2024.0329     0.03381961 -32.167768 32.235407 -49.214259 49.281898
## 2024.0356     0.03381961 -32.222982 32.290621 -49.298701 49.366340
## 2024.0384     0.03381961 -32.278101 32.345740 -49.382999 49.450638
## 2024.0411     0.03381961 -32.333127 32.400766 -49.467153 49.534792
## 2024.0438     0.03381961 -32.388059 32.455698 -49.551164 49.618804
## 2024.0466     0.03381961 -32.442898 32.510537 -49.635034 49.702673
## 2024.0493     0.03381961 -32.497645 32.565284 -49.718762 49.786401
## 2024.0521     0.03381961 -32.552300 32.619939 -49.802349 49.869988
## 2024.0548     0.03381961 -32.606863 32.674502 -49.885796 49.953436
## 2024.0575     0.03381961 -32.661335 32.728974 -49.969104 50.036744
## 2024.0603     0.03381961 -32.715717 32.783356 -50.052274 50.119913
## 2024.0630     0.03381961 -32.770008 32.837647 -50.135305 50.202945
## 2024.0658     0.03381961 -32.824210 32.891849 -50.218200 50.285839
## 2024.0685     0.03381961 -32.878322 32.945962 -50.300958 50.368597
## 2024.0712     0.03381961 -32.932346 32.999985 -50.383580 50.451219
## 2024.0740     0.03381961 -32.986281 33.053920 -50.466067 50.533706
## 2024.0767     0.03381961 -33.040129 33.107768 -50.548419 50.616058
## 2024.0795     0.03381961 -33.093888 33.161528 -50.630638 50.698277
## 2024.0822     0.03381961 -33.147561 33.215200 -50.712723 50.780362
## 2024.0849     0.03381961 -33.201147 33.268786 -50.794676 50.862315
## 2024.0877     0.03381961 -33.254647 33.322286 -50.876496 50.944136
## 2024.0904     0.03381961 -33.308061 33.375700 -50.958186 51.025825
## 2024.0932     0.03381961 -33.361389 33.429028 -51.039745 51.107384
## 2024.0959     0.03381961 -33.414633 33.482272 -51.121174 51.188813
## 2024.0986     0.03381961 -33.467791 33.535431 -51.202473 51.270112
## 2024.1014     0.03381961 -33.520866 33.588505 -51.283644 51.351283
## 2024.1041     0.03381961 -33.573857 33.641496 -51.364686 51.432325
## 2024.1068     0.03381961 -33.626764 33.694404 -51.445601 51.513240
## 2024.1096     0.03381961 -33.679589 33.747228 -51.526389 51.594028
## 2024.1123     0.03381961 -33.732330 33.799970 -51.607050 51.674690
## 2024.1151     0.03381961 -33.784990 33.852629 -51.687586 51.755225
## 2024.1178     0.03381961 -33.837567 33.905207 -51.767997 51.835636
## 2024.1205     0.03381961 -33.890063 33.957703 -51.848282 51.915922
## 2024.1233     0.03381961 -33.942478 34.010118 -51.928444 51.996083
## 2024.1260     0.03381961 -33.994813 34.062452 -52.008483 52.076122
## 2024.1288     0.03381961 -34.047067 34.114706 -52.088398 52.156037
## 2024.1315     0.03381961 -34.099241 34.166880 -52.168191 52.235830
## 2024.1342     0.03381961 -34.151335 34.218974 -52.247862 52.315502
## 2024.1370     0.03381961 -34.203350 34.270989 -52.327412 52.395052
## 2024.1397     0.03381961 -34.255286 34.322925 -52.406842 52.474481
## 2024.1425     0.03381961 -34.307143 34.374783 -52.486151 52.553790
## 2024.1452     0.03381961 -34.358923 34.426562 -52.565341 52.632980
## 2024.1479     0.03381961 -34.410624 34.478264 -52.644412 52.712051
## 2024.1507     0.03381961 -34.462248 34.529888 -52.723364 52.791003
## 2024.1534     0.03381961 -34.513795 34.581434 -52.802198 52.869837
## 2024.1562     0.03381961 -34.565265 34.632905 -52.880915 52.948554
## 2024.1589     0.03381961 -34.616659 34.684298 -52.959514 53.027154
## 2024.1616     0.03381961 -34.667977 34.735616 -53.037998 53.105637
## 2024.1644     0.03381961 -34.719218 34.786857 -53.116365 53.184004
## 2024.1671     0.03381961 -34.770385 34.838024 -53.194617 53.262257
## 2024.1699     0.03381961 -34.821476 34.889115 -53.272755 53.340394
## 2024.1726     0.03381961 -34.872492 34.940131 -53.350777 53.418417
## 2024.1753     0.03381961 -34.923434 34.991073 -53.428686 53.496326
## 2024.1781     0.03381961 -34.974302 35.041941 -53.506482 53.574121
## 2024.1808     0.03381961 -35.025096 35.092735 -53.584165 53.651804
## 2024.1836     0.03381961 -35.075817 35.143456 -53.661735 53.729375
## 2024.1863     0.03381961 -35.126464 35.194103 -53.739194 53.806833
## 2024.1890     0.03381961 -35.177038 35.244678 -53.816541 53.884180
## 2024.1918     0.03381961 -35.227540 35.295180 -53.893777 53.961416
## 2024.1945     0.03381961 -35.277970 35.345609 -53.970903 54.038542
## 2024.1973     0.03381961 -35.328328 35.395967 -54.047918 54.115558
## 2024.2000     0.03381961 -35.378614 35.446254 -54.124824 54.192464
## 2024.2027     0.03381961 -35.428829 35.496468 -54.201622 54.269261
## 2024.2055     0.03381961 -35.478973 35.546612 -54.278310 54.345949
## 2024.2082     0.03381961 -35.529046 35.596686 -54.354891 54.422530
## 2024.2110     0.03381961 -35.579049 35.646688 -54.431363 54.499002
## 2024.2137     0.03381961 -35.628982 35.696621 -54.507729 54.575368
## 2024.2164     0.03381961 -35.678845 35.746484 -54.583987 54.651627
## 2024.2192     0.03381961 -35.728638 35.796277 -54.660140 54.727779
## 2024.2219     0.03381961 -35.778362 35.846002 -54.736186 54.803826
## 2024.2247     0.03381961 -35.828018 35.895657 -54.812127 54.879767
## 2024.2274     0.03381961 -35.877604 35.945243 -54.887963 54.955603
## 2024.2301     0.03381961 -35.927122 35.994761 -54.963695 55.031334
## 2024.2329     0.03381961 -35.976572 36.044212 -55.039322 55.106962
## 2024.2356     0.03381961 -36.025955 36.093594 -55.114846 55.182485
## 2024.2384     0.03381961 -36.075269 36.142909 -55.190266 55.257906
## 2024.2411     0.03381961 -36.124517 36.192156 -55.265584 55.333223
## 2024.2438     0.03381961 -36.173697 36.241336 -55.340799 55.408438
## 2024.2466     0.03381961 -36.222811 36.290450 -55.415912 55.483551
## 2024.2493     0.03381961 -36.271858 36.339498 -55.490923 55.558563
## 2024.2521     0.03381961 -36.320839 36.388479 -55.565833 55.633473
## 2024.2548     0.03381961 -36.369755 36.437394 -55.640643 55.708282
## 2024.2575     0.03381961 -36.418604 36.486244 -55.715352 55.782991
## 2024.2603     0.03381961 -36.467389 36.535028 -55.789961 55.857600
## 2024.2630     0.03381961 -36.516108 36.583747 -55.864470 55.932110

print(ses_model$mean)

## Time Series:
## Start = c(2023, 90) 
## End = c(2024, 97) 
## Frequency = 365 
##   [1] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
##   [7] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
##  [13] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
##  [19] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
##  [25] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
##  [31] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
##  [37] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
##  [43] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
##  [49] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
##  [55] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
##  [61] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
##  [67] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
##  [73] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
##  [79] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
##  [85] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
##  [91] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
##  [97] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [103] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [109] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [115] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [121] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [127] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [133] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [139] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [145] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [151] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [157] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [163] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [169] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [175] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [181] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [187] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [193] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [199] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [205] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [211] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [217] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [223] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [229] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [235] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [241] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [247] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [253] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [259] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [265] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [271] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [277] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [283] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [289] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [295] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [301] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [307] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [313] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [319] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [325] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [331] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [337] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [343] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [349] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [355] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [361] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [367] 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961 0.03381961
## [373] 0.03381961

test_acc_ses <- accuracy(ses_model, x = regular_ts)
print(test_acc_ses)

##                        ME      RMSE       MAE  MPE MAPE       MASE       ACF1
## Training set -0.001793513 2.6947873 1.3097913 -Inf  Inf 0.41689898 0.10171796
## Test set      0.043928379 0.3083515 0.1070341 -Inf  Inf 0.03406834 0.05005751
##              Theil's U
## Training set        NA
## Test set             0

ses_ts_plot <- autoplot(train) +
  autolayer(ses_model, PI = FALSE, size = 1.1, series = 'SES Model') +
  autolayer(test, series = 'Test Data')

Regular TS-holt’s

holt_model <- holt(train, h = length(test))
holt_text_file_name <- paste0(character_name, "_holt_model_output.txt")

print(holt_model)

##           Point Forecast      Lo 80     Hi 80      Lo 95     Hi 95
## 2023.2438   0.0311259561  -3.430586  3.492838  -5.263106  5.325358
## 2023.2466   0.0297556091  -3.915245  3.974756  -6.003602  6.063113
## 2023.2493   0.0283852622  -4.346990  4.403761  -6.663174  6.719945
## 2023.2521   0.0270149153  -4.740176  4.794206  -7.263774  7.317804
## 2023.2548   0.0256445684  -5.103645  5.154934  -7.818927  7.870216
## 2023.2575   0.0242742215  -5.443305  5.491854  -8.337667  8.386216
## 2023.2603   0.0229038746  -5.763335  5.809142  -8.826384  8.872192
## 2023.2630   0.0215335276  -6.066815  6.109882  -9.289793  9.332860
## 2023.2658   0.0201631807  -6.356101  6.396427  -9.731491  9.771817
## 2023.2685   0.0187928338  -6.633034  6.670620 -10.154299 10.191885
## 2023.2712   0.0174224869  -6.899092  6.933937 -10.560474 10.595319
## 2023.2740   0.0160521400  -7.155479  7.187584 -10.951859 10.983963
## 2023.2767   0.0146817931  -7.403193  7.432556 -11.329978 11.359342
## 2023.2795   0.0133114461  -7.643070  7.669693 -11.696113 11.722736
## 2023.2822   0.0119410992  -7.875821  7.899704 -12.051351 12.075233
## 2023.2849   0.0105707523  -8.102057  8.123199 -12.396623 12.417765
## 2023.2877   0.0092004054  -8.322305  8.340706 -12.732738 12.751139
## 2023.2904   0.0078300585  -8.537025  8.552685 -13.060398 13.076058
## 2023.2932   0.0064597116  -8.746621  8.759541 -13.380223 13.393142
## 2023.2959   0.0050893646  -8.951451  8.961630 -13.692757 13.702936
## 2023.2986   0.0037190177  -9.151833  9.159271 -13.998489 14.005927
## 2023.3014   0.0023486708  -9.348050  9.352747 -14.297851 14.302549
## 2023.3041   0.0009783239  -9.540357  9.542314 -14.591235 14.593192
## 2023.3068  -0.0003920230  -9.728986  9.728202 -14.878992 14.878208
## 2023.3096  -0.0017623699  -9.914144  9.910619 -15.161441 15.157917
## 2023.3123  -0.0031327169 -10.096021 10.089755 -15.438873 15.432607
## 2023.3151  -0.0045030638 -10.274789 10.265783 -15.711551 15.702545
## 2023.3178  -0.0058734107 -10.450609 10.438862 -15.979718 15.967971
## 2023.3205  -0.0072437576 -10.623624 10.609136 -16.243596 16.229109
## 2023.3233  -0.0086141045 -10.793969 10.776740 -16.503391 16.486162
## 2023.3260  -0.0099844515 -10.961767 10.941798 -16.759290 16.739321
## 2023.3288  -0.0113547984 -11.127133 11.104423 -17.011470 16.988760
## 2023.3315  -0.0127251453 -11.290172 11.264722 -17.260092 17.234642
## 2023.3342  -0.0140954922 -11.450985 11.422794 -17.505308 17.477117
## 2023.3370  -0.0154658391 -11.609661 11.578729 -17.747257 17.716326
## 2023.3397  -0.0168361860 -11.766288 11.732616 -17.986072 17.952400
## 2023.3425  -0.0182065330 -11.920945 11.884532 -18.221874 18.185461
## 2023.3452  -0.0195768799 -12.073708 12.034554 -18.454779 18.415626
## 2023.3479  -0.0209472268 -12.224647 12.182752 -18.684895 18.643001
## 2023.3507  -0.0223175737 -12.373828 12.329193 -18.912322 18.867687
## 2023.3534  -0.0236879206 -12.521314 12.473938 -19.137157 19.089781
## 2023.3562  -0.0250582675 -12.667163 12.617047 -19.359489 19.309373
## 2023.3589  -0.0264286145 -12.811432 12.758574 -19.579403 19.526546
## 2023.3616  -0.0277989614 -12.954171 12.898573 -19.796980 19.741382
## 2023.3644  -0.0291693083 -13.095432 13.037094 -20.012294 19.953955
## 2023.3671  -0.0305396552 -13.235261 13.174182 -20.225419 20.164339
## 2023.3699  -0.0319100021 -13.373703 13.309883 -20.436421 20.372601
## 2023.3726  -0.0332803490 -13.510799 13.444239 -20.645367 20.578806
## 2023.3753  -0.0346506960 -13.646591 13.577290 -20.852318 20.783016
## 2023.3781  -0.0360210429 -13.781117 13.709075 -21.057331 20.985289
## 2023.3808  -0.0373913898 -13.914412 13.839629 -21.260463 21.185681
## 2023.3836  -0.0387617367 -14.046512 13.968989 -21.461768 21.384244
## 2023.3863  -0.0401320836 -14.177451 14.097186 -21.661295 21.581031
## 2023.3890  -0.0415024305 -14.307258 14.224253 -21.859093 21.776088
## 2023.3918  -0.0428727775 -14.435966 14.350220 -22.055209 21.969463
## 2023.3945  -0.0442431244 -14.563602 14.475116 -22.249687 22.161200
## 2023.3973  -0.0456134713 -14.690195 14.598968 -22.442568 22.351341
## 2023.4000  -0.0469838182 -14.815771 14.721804 -22.633895 22.539927
## 2023.4027  -0.0483541651 -14.940356 14.843647 -22.823705 22.726997
## 2023.4055  -0.0497245120 -15.063973 14.964524 -23.012036 22.912587
## 2023.4082  -0.0510948590 -15.186647 15.084457 -23.198925 23.096735
## 2023.4110  -0.0524652059 -15.308400 15.203470 -23.384404 23.279474
## 2023.4137  -0.0538355528 -15.429253 15.321582 -23.568508 23.460837
## 2023.4164  -0.0552058997 -15.549228 15.438816 -23.751268 23.640856
## 2023.4192  -0.0565762466 -15.668344 15.555192 -23.932715 23.819563
## 2023.4219  -0.0579465936 -15.786621 15.670728 -24.112879 23.996986
## 2023.4247  -0.0593169405 -15.904077 15.785444 -24.291787 24.173153
## 2023.4274  -0.0606872874 -16.020731 15.899356 -24.469467 24.348093
## 2023.4301  -0.0620576343 -16.136599 16.012483 -24.645947 24.521831
## 2023.4329  -0.0634279812 -16.251698 16.124842 -24.821250 24.694394
## 2023.4356  -0.0647983281 -16.366044 16.236447 -24.995402 24.865805
## 2023.4384  -0.0661686751 -16.479653 16.347315 -25.168427 25.036089
## 2023.4411  -0.0675390220 -16.592540 16.457462 -25.340347 25.205269
## 2023.4438  -0.0689093689 -16.704719 16.566900 -25.511185 25.373366
## 2023.4466  -0.0702797158 -16.816205 16.675645 -25.680962 25.540402
## 2023.4493  -0.0716500627 -16.927010 16.783710 -25.849699 25.706399
## 2023.4521  -0.0730204096 -17.037149 16.891108 -26.017416 25.871376
## 2023.4548  -0.0743907566 -17.146634 16.997852 -26.184133 26.035352
## 2023.4575  -0.0757611035 -17.255477 17.103955 -26.349869 26.198347
## 2023.4603  -0.0771314504 -17.363690 17.209427 -26.514642 26.360379
## 2023.4630  -0.0785017973 -17.471286 17.314282 -26.678469 26.521465
## 2023.4658  -0.0798721442 -17.578274 17.418530 -26.841368 26.681624
## 2023.4685  -0.0812424911 -17.684666 17.522181 -27.003356 26.840871
## 2023.4712  -0.0826128381 -17.790473 17.625248 -27.164449 26.999223
## 2023.4740  -0.0839831850 -17.895706 17.727739 -27.324662 27.156695
## 2023.4767  -0.0853535319 -18.000373 17.829666 -27.484011 27.313304
## 2023.4795  -0.0867238788 -18.104484 17.931037 -27.642511 27.469063
## 2023.4822  -0.0880942257 -18.208050 18.031862 -27.800176 27.623987
## 2023.4849  -0.0894645726 -18.311080 18.132151 -27.957020 27.778091
## 2023.4877  -0.0908349196 -18.413581 18.231912 -28.113057 27.931388
## 2023.4904  -0.0922052665 -18.515564 18.331153 -28.268301 28.083890
## 2023.4932  -0.0935756134 -18.617036 18.429885 -28.422764 28.235613
## 2023.4959  -0.0949459603 -18.718006 18.528114 -28.576458 28.386566
## 2023.4986  -0.0963163072 -18.818481 18.625849 -28.729397 28.536764
## 2023.5014  -0.0976866542 -18.918470 18.723097 -28.881592 28.686218
## 2023.5041  -0.0990570011 -19.017981 18.819867 -29.033054 28.834940
## 2023.5068  -0.1004273480 -19.117019 18.916165 -29.183795 28.982940
## 2023.5096  -0.1017976949 -19.215594 19.011999 -29.333826 29.130231
## 2023.5123  -0.1031680418 -19.313711 19.107375 -29.483159 29.276823
## 2023.5151  -0.1045383887 -19.411378 19.202302 -29.631802 29.422726
## 2023.5178  -0.1059087357 -19.508602 19.296785 -29.779768 29.567950
## 2023.5205  -0.1072790826 -19.605389 19.390831 -29.927064 29.712506
## 2023.5233  -0.1086494295 -19.701745 19.484446 -30.073703 29.856404
## 2023.5260  -0.1100197764 -19.797676 19.577637 -30.219692 29.999652
## 2023.5288  -0.1113901233 -19.893190 19.670409 -30.365042 30.142261
## 2023.5315  -0.1127604702 -19.988290 19.762770 -30.509761 30.284240
## 2023.5342  -0.1141308172 -20.082985 19.854723 -30.653858 30.425596
## 2023.5370  -0.1155011641 -20.177279 19.946276 -30.797342 30.566340
## 2023.5397  -0.1168715110 -20.271177 20.037434 -30.940222 30.706479
## 2023.5425  -0.1182418579 -20.364685 20.128202 -31.082505 30.846021
## 2023.5452  -0.1196122048 -20.457809 20.218585 -31.224200 30.984976
## 2023.5479  -0.1209825517 -20.550554 20.308588 -31.365315 31.123350
## 2023.5507  -0.1223528987 -20.642924 20.398218 -31.505858 31.261152
## 2023.5534  -0.1237232456 -20.734925 20.487478 -31.645835 31.398389
## 2023.5562  -0.1250935925 -20.826561 20.576374 -31.785256 31.535069
## 2023.5589  -0.1264639394 -20.917838 20.664910 -31.924126 31.671198
## 2023.5616  -0.1278342863 -21.008759 20.753091 -32.062453 31.806784
## 2023.5644  -0.1292046332 -21.099330 20.840921 -32.200244 31.941835
## 2023.5671  -0.1305749802 -21.189555 20.928405 -32.337506 32.076356
## 2023.5699  -0.1319453271 -21.279438 21.015548 -32.474245 32.210354
## 2023.5726  -0.1333156740 -21.368984 21.102353 -32.610468 32.343837
## 2023.5753  -0.1346860209 -21.458197 21.188825 -32.746181 32.476809
## 2023.5781  -0.1360563678 -21.547080 21.274968 -32.881392 32.609279
## 2023.5808  -0.1374267148 -21.635639 21.360785 -33.016105 32.741251
## 2023.5836  -0.1387970617 -21.723876 21.446282 -33.150326 32.872732
## 2023.5863  -0.1401674086 -21.811796 21.531461 -33.284063 33.003728
## 2023.5890  -0.1415377555 -21.899402 21.616327 -33.417320 33.134245
## 2023.5918  -0.1429081024 -21.986699 21.700883 -33.550103 33.264287
## 2023.5945  -0.1442784493 -22.073690 21.785133 -33.682419 33.393862
## 2023.5973  -0.1456487963 -22.160378 21.869080 -33.814271 33.522974
## 2023.6000  -0.1470191432 -22.246767 21.952728 -33.945666 33.651628
## 2023.6027  -0.1483894901 -22.332860 22.036081 -34.076609 33.779830
## 2023.6055  -0.1497598370 -22.418661 22.119141 -34.207105 33.907586
## 2023.6082  -0.1511301839 -22.504173 22.201913 -34.337160 34.034899
## 2023.6110  -0.1525005308 -22.589400 22.284399 -34.466777 34.161776
## 2023.6137  -0.1538708778 -22.674344 22.366603 -34.595963 34.288221
## 2023.6164  -0.1552412247 -22.759009 22.448527 -34.724721 34.414239
## 2023.6192  -0.1566115716 -22.843398 22.530175 -34.853057 34.539834
## 2023.6219  -0.1579819185 -22.927513 22.611549 -34.980975 34.665011
## 2023.6247  -0.1593522654 -23.011358 22.692654 -35.108480 34.789775
## 2023.6274  -0.1607226123 -23.094936 22.773491 -35.235576 34.914131
## 2023.6301  -0.1620929593 -23.178250 22.854064 -35.362267 35.038081
## 2023.6329  -0.1634633062 -23.261302 22.934375 -35.488559 35.161632
## 2023.6356  -0.1648336531 -23.344095 23.014427 -35.614454 35.284787
## 2023.6384  -0.1662040000 -23.426632 23.094224 -35.739958 35.407550
## 2023.6411  -0.1675743469 -23.508915 23.173766 -35.865074 35.529926
## 2023.6438  -0.1689446938 -23.590948 23.253058 -35.989807 35.651918
## 2023.6466  -0.1703150408 -23.672732 23.332102 -36.114160 35.773530
## 2023.6493  -0.1716853877 -23.754271 23.410900 -36.238137 35.894767
## 2023.6521  -0.1730557346 -23.835566 23.489455 -36.361743 36.015631
## 2023.6548  -0.1744260815 -23.916621 23.567769 -36.484980 36.136128
## 2023.6575  -0.1757964284 -23.997438 23.645845 -36.607853 36.256260
## 2023.6603  -0.1771667753 -24.078018 23.723685 -36.730365 36.376031
## 2023.6630  -0.1785371223 -24.158365 23.801291 -36.852519 36.495445
## 2023.6658  -0.1799074692 -24.238481 23.878666 -36.974320 36.614505
## 2023.6685  -0.1812778161 -24.318368 23.955812 -37.095771 36.733215
## 2023.6712  -0.1826481630 -24.398028 24.032731 -37.216875 36.851579
## 2023.6740  -0.1840185099 -24.477463 24.109426 -37.337636 36.969599
## 2023.6767  -0.1853888569 -24.556676 24.185898 -37.458056 37.087278
## 2023.6795  -0.1867592038 -24.635669 24.262150 -37.578140 37.204621
## 2023.6822  -0.1881295507 -24.714443 24.338184 -37.697889 37.321630
## 2023.6849  -0.1894998976 -24.793002 24.414002 -37.817309 37.438309
## 2023.6877  -0.1908702445 -24.871346 24.489605 -37.936401 37.554660
## 2023.6904  -0.1922405914 -24.949478 24.564997 -38.055168 37.670687
## 2023.6932  -0.1936109384 -25.027400 24.640178 -38.173614 37.786392
## 2023.6959  -0.1949812853 -25.105114 24.715152 -38.291742 37.901780
## 2023.6986  -0.1963516322 -25.182622 24.789919 -38.409554 38.016851
## 2023.7014  -0.1977219791 -25.259925 24.864481 -38.527054 38.131610
## 2023.7041  -0.1990923260 -25.337026 24.938841 -38.644244 38.246060
## 2023.7068  -0.2004626729 -25.413926 25.013001 -38.761127 38.360202
## 2023.7096  -0.2018330199 -25.490627 25.086961 -38.877706 38.474040
## 2023.7123  -0.2032033668 -25.567131 25.160725 -38.993984 38.587577
## 2023.7151  -0.2045737137 -25.643440 25.234293 -39.109963 38.700815
## 2023.7178  -0.2059440606 -25.719555 25.307667 -39.225645 38.813757
## 2023.7205  -0.2073144075 -25.795479 25.380850 -39.341034 38.926406
## 2023.7233  -0.2086847544 -25.871212 25.453842 -39.456133 39.038763
## 2023.7260  -0.2100551014 -25.946756 25.526646 -39.570942 39.150832
## 2023.7288  -0.2114254483 -26.022113 25.599262 -39.685466 39.262615
## 2023.7315  -0.2127957952 -26.097285 25.671694 -39.799706 39.374115
## 2023.7342  -0.2141661421 -26.172274 25.743941 -39.913666 39.485333
## 2023.7370  -0.2155364890 -26.247080 25.816007 -40.027346 39.596273
## 2023.7397  -0.2169068359 -26.321705 25.887891 -40.140750 39.706937
## 2023.7425  -0.2182771829 -26.396151 25.959597 -40.253881 39.817326
## 2023.7452  -0.2196475298 -26.470420 26.031125 -40.366739 39.927444
## 2023.7479  -0.2210178767 -26.544512 26.102476 -40.479328 40.037293
## 2023.7507  -0.2223882236 -26.618430 26.173653 -40.591650 40.146874
## 2023.7534  -0.2237585705 -26.692174 26.244657 -40.703707 40.256190
## 2023.7562  -0.2251289175 -26.765747 26.315489 -40.815501 40.365244
## 2023.7589  -0.2264992644 -26.839149 26.386151 -40.927035 40.474036
## 2023.7616  -0.2278696113 -26.912382 26.456643 -41.038310 40.582571
## 2023.7644  -0.2292399582 -26.985448 26.526968 -41.149328 40.690849
## 2023.7671  -0.2306103051 -27.058347 26.597126 -41.260093 40.798872
## 2023.7699  -0.2319806520 -27.131081 26.667120 -41.370604 40.906643
## 2023.7726  -0.2333509990 -27.203651 26.736949 -41.480866 41.014164
## 2023.7753  -0.2347213459 -27.276059 26.806617 -41.590879 41.121436
## 2023.7781  -0.2360916928 -27.348306 26.876123 -41.700645 41.228462
## 2023.7808  -0.2374620397 -27.420393 26.945469 -41.810168 41.335244
## 2023.7836  -0.2388323866 -27.492322 27.014657 -41.919447 41.441782
## 2023.7863  -0.2402027335 -27.564093 27.083687 -42.028486 41.548081
## 2023.7890  -0.2415730805 -27.635708 27.152561 -42.137286 41.654140
## 2023.7918  -0.2429434274 -27.707168 27.221281 -42.245850 41.759963
## 2023.7945  -0.2443137743 -27.778474 27.289846 -42.354178 41.865550
## 2023.7973  -0.2456841212 -27.849627 27.358259 -42.462272 41.970904
## 2023.8000  -0.2470544681 -27.920630 27.426521 -42.570135 42.076026
## 2023.8027  -0.2484248150 -27.991481 27.494632 -42.677768 42.180919
## 2023.8055  -0.2497951620 -28.062184 27.562594 -42.785174 42.285583
## 2023.8082  -0.2511655089 -28.132739 27.630408 -42.892352 42.390021
## 2023.8110  -0.2525358558 -28.203147 27.698075 -42.999306 42.494235
## 2023.8137  -0.2539062027 -28.273409 27.765596 -43.106037 42.598225
## 2023.8164  -0.2552765496 -28.343526 27.832973 -43.212547 42.701994
## 2023.8192  -0.2566468965 -28.413499 27.900205 -43.318837 42.805543
## 2023.8219  -0.2580172435 -28.483330 27.967296 -43.424908 42.908874
## 2023.8247  -0.2593875904 -28.553019 28.034244 -43.530763 43.011988
## 2023.8274  -0.2607579373 -28.622568 28.101052 -43.636403 43.114887
## 2023.8301  -0.2621282842 -28.691977 28.167720 -43.741830 43.217573
## 2023.8329  -0.2634986311 -28.761247 28.234250 -43.847044 43.320047
## 2023.8356  -0.2648689781 -28.830380 28.300642 -43.952049 43.422311
## 2023.8384  -0.2662393250 -28.899377 28.366898 -44.056844 43.524366
## 2023.8411  -0.2676096719 -28.968238 28.433018 -44.161432 43.626213
## 2023.8438  -0.2689800188 -29.036964 28.499004 -44.265814 43.727854
## 2023.8466  -0.2703503657 -29.105556 28.564855 -44.369992 43.829291
## 2023.8493  -0.2717207126 -29.174016 28.630574 -44.473966 43.930525
## 2023.8521  -0.2730910596 -29.242343 28.696161 -44.577739 44.031557
## 2023.8548  -0.2744614065 -29.310540 28.761617 -44.681312 44.132389
## 2023.8575  -0.2758317534 -29.378607 28.826943 -44.784685 44.233022
## 2023.8603  -0.2772021003 -29.446544 28.892140 -44.887862 44.333457
## 2023.8630  -0.2785724472 -29.514354 28.957209 -44.990842 44.433697
## 2023.8658  -0.2799427941 -29.582036 29.022150 -45.093627 44.533741
## 2023.8685  -0.2813131411 -29.649591 29.086965 -45.196219 44.633593
## 2023.8712  -0.2826834880 -29.717021 29.151654 -45.298619 44.733252
## 2023.8740  -0.2840538349 -29.784326 29.216219 -45.400827 44.832720
## 2023.8767  -0.2854241818 -29.851508 29.280659 -45.502847 44.931998
## 2023.8795  -0.2867945287 -29.918566 29.344977 -45.604678 45.031089
## 2023.8822  -0.2881648756 -29.985501 29.409172 -45.706322 45.129992
## 2023.8849  -0.2895352226 -30.052316 29.473245 -45.807780 45.228709
## 2023.8877  -0.2909055695 -30.119009 29.537198 -45.909053 45.327242
## 2023.8904  -0.2922759164 -30.185583 29.601031 -46.010143 45.425592
## 2023.8932  -0.2936462633 -30.252037 29.664745 -46.111051 45.523759
## 2023.8959  -0.2950166102 -30.318373 29.728340 -46.211778 45.621745
## 2023.8986  -0.2963869571 -30.384592 29.791818 -46.312326 45.719552
## 2023.9014  -0.2977573041 -30.450694 29.855179 -46.412694 45.817180
## 2023.9041  -0.2991276510 -30.516680 29.918424 -46.512885 45.914630
## 2023.9068  -0.3004979979 -30.582550 29.981554 -46.612900 46.011904
## 2023.9096  -0.3018683448 -30.648306 30.044569 -46.712740 46.109003
## 2023.9123  -0.3032386917 -30.713948 30.107471 -46.812405 46.205928
## 2023.9151  -0.3046090386 -30.779477 30.170259 -46.911898 46.302680
## 2023.9178  -0.3059793856 -30.844894 30.232935 -47.011219 46.399260
## 2023.9205  -0.3073497325 -30.910199 30.295499 -47.110369 46.495669
## 2023.9233  -0.3087200794 -30.975393 30.357953 -47.209349 46.591909
## 2023.9260  -0.3100904263 -31.040477 30.420296 -47.308160 46.687980
## 2023.9288  -0.3114607732 -31.105451 30.482529 -47.406804 46.783883
## 2023.9315  -0.3128311202 -31.170316 30.544654 -47.505282 46.879620
## 2023.9342  -0.3142014671 -31.235073 30.606670 -47.603594 46.975191
## 2023.9370  -0.3155718140 -31.299722 30.668579 -47.701741 47.070597
## 2023.9397  -0.3169421609 -31.364265 30.730381 -47.799725 47.165841
## 2023.9425  -0.3183125078 -31.428701 30.792076 -47.897546 47.260921
## 2023.9452  -0.3196828547 -31.493032 30.853666 -47.995206 47.355840
## 2023.9479  -0.3210532017 -31.557258 30.915151 -48.092706 47.450599
## 2023.9507  -0.3224235486 -31.621379 30.976532 -48.190045 47.545198
## 2023.9534  -0.3237938955 -31.685397 31.037809 -48.287227 47.639639
## 2023.9562  -0.3251642424 -31.749311 31.098983 -48.384250 47.733922
## 2023.9589  -0.3265345893 -31.813124 31.160055 -48.481117 47.828048
## 2023.9616  -0.3279049362 -31.876834 31.221024 -48.577828 47.922018
## 2023.9644  -0.3292752832 -31.940443 31.281893 -48.674385 48.015834
## 2023.9671  -0.3306456301 -32.003952 31.342661 -48.770787 48.109496
## 2023.9699  -0.3320159770 -32.067360 31.403328 -48.867037 48.203005
## 2023.9726  -0.3333863239 -32.130669 31.463897 -48.963134 48.296362
## 2023.9753  -0.3347566708 -32.193880 31.524366 -49.059080 48.389567
## 2023.9781  -0.3361270177 -32.256991 31.584737 -49.154876 48.482622
## 2023.9808  -0.3374973647 -32.320006 31.645011 -49.250523 48.575528
## 2023.9836  -0.3388677116 -32.382923 31.705187 -49.346021 48.668285
## 2023.9863  -0.3402380585 -32.445743 31.765267 -49.441371 48.760895
## 2023.9890  -0.3416084054 -32.508468 31.825251 -49.536574 48.853357
## 2023.9918  -0.3429787523 -32.571097 31.885139 -49.631632 48.945674
## 2023.9945  -0.3443490992 -32.633631 31.944932 -49.726544 49.037846
## 2023.9973  -0.3457194462 -32.696070 32.004631 -49.821312 49.129873
## 2024.0000  -0.3470897931 -32.758416 32.064237 -49.915936 49.221756
## 2024.0027  -0.3484601400 -32.820669 32.123748 -50.010418 49.313497
## 2024.0055  -0.3498304869 -32.882828 32.183167 -50.104757 49.405096
## 2024.0082  -0.3512008338 -32.944896 32.242494 -50.198956 49.496554
## 2024.0110  -0.3525711808 -33.006872 32.301729 -50.293014 49.587872
## 2024.0137  -0.3539415277 -33.068756 32.360873 -50.386933 49.679050
## 2024.0164  -0.3553118746 -33.130550 32.419926 -50.480713 49.770089
## 2024.0192  -0.3566822215 -33.192254 32.478889 -50.574355 49.860991
## 2024.0219  -0.3580525684 -33.253867 32.537762 -50.667860 49.951755
## 2024.0247  -0.3594229153 -33.315392 32.596546 -50.761228 50.042382
## 2024.0274  -0.3607932623 -33.376828 32.655241 -50.854461 50.132874
## 2024.0301  -0.3621636092 -33.438176 32.713848 -50.947559 50.223232
## 2024.0329  -0.3635339561 -33.499436 32.772368 -51.040522 50.313454
## 2024.0356  -0.3649043030 -33.560608 32.830800 -51.133352 50.403544
## 2024.0384  -0.3662746499 -33.621694 32.889145 -51.226050 50.493500
## 2024.0411  -0.3676449968 -33.682693 32.947404 -51.318615 50.583325
## 2024.0438  -0.3690153438 -33.743607 33.005576 -51.411049 50.673018
## 2024.0466  -0.3703856907 -33.804435 33.063664 -51.503352 50.762581
## 2024.0493  -0.3717560376 -33.865179 33.121667 -51.595526 50.852013
## 2024.0521  -0.3731263845 -33.925837 33.179585 -51.687570 50.941317
## 2024.0548  -0.3744967314 -33.986412 33.237419 -51.779485 51.030492
## 2024.0575  -0.3758670783 -34.046903 33.295169 -51.871273 51.119539
## 2024.0603  -0.3772374253 -34.107311 33.352836 -51.962934 51.208459
## 2024.0630  -0.3786077722 -34.167637 33.410421 -52.054468 51.297252
## 2024.0658  -0.3799781191 -34.227880 33.467923 -52.145876 51.385920
## 2024.0685  -0.3813484660 -34.288041 33.525344 -52.237159 51.474462
## 2024.0712  -0.3827188129 -34.348120 33.582683 -52.328318 51.562880
## 2024.0740  -0.3840891598 -34.408119 33.639941 -52.419353 51.651174
## 2024.0767  -0.3854595068 -34.468037 33.697118 -52.510264 51.739345
## 2024.0795  -0.3868298537 -34.527875 33.754216 -52.601053 51.827393
## 2024.0822  -0.3882002006 -34.587634 33.811233 -52.691720 51.915320
## 2024.0849  -0.3895705475 -34.647313 33.868171 -52.782266 52.003125
## 2024.0877  -0.3909408944 -34.706913 33.925031 -52.872691 52.090809
## 2024.0904  -0.3923112414 -34.766434 33.981812 -52.962996 52.178373
## 2024.0932  -0.3936815883 -34.825877 34.038514 -53.053181 52.265818
## 2024.0959  -0.3950519352 -34.885243 34.095139 -53.143248 52.353144
## 2024.0986  -0.3964222821 -34.944532 34.151687 -53.233196 52.440351
## 2024.1014  -0.3977926290 -35.003743 34.208158 -53.323026 52.527441
## 2024.1041  -0.3991629759 -35.062878 34.264552 -53.412740 52.614414
## 2024.1068  -0.4005333229 -35.121937 34.320870 -53.502337 52.701271
## 2024.1096  -0.4019036698 -35.180920 34.377112 -53.591818 52.788011
## 2024.1123  -0.4032740167 -35.239827 34.433279 -53.681184 52.874636
## 2024.1151  -0.4046443636 -35.298660 34.489371 -53.770436 52.961147
## 2024.1178  -0.4060147105 -35.357418 34.545388 -53.859573 53.047543
## 2024.1205  -0.4073850574 -35.416101 34.601331 -53.948596 53.133826
## 2024.1233  -0.4087554044 -35.474711 34.657200 -54.037507 53.219996
## 2024.1260  -0.4101257513 -35.533247 34.712996 -54.126305 53.306053
## 2024.1288  -0.4114960982 -35.591710 34.768718 -54.214991 53.391999
## 2024.1315  -0.4128664451 -35.650100 34.824368 -54.303565 53.477833
## 2024.1342  -0.4142367920 -35.708418 34.879945 -54.392029 53.563556
## 2024.1370  -0.4156071389 -35.766664 34.935450 -54.480383 53.649169
## 2024.1397  -0.4169774859 -35.824838 34.990883 -54.568627 53.734672
## 2024.1425  -0.4183478328 -35.882940 35.046245 -54.656761 53.820066
## 2024.1452  -0.4197181797 -35.940972 35.101535 -54.744787 53.905351
## 2024.1479  -0.4210885266 -35.998932 35.156755 -54.832705 53.990528
## 2024.1507  -0.4224588735 -36.056823 35.211905 -54.920515 54.075598
## 2024.1534  -0.4238292204 -36.114643 35.266984 -55.008218 54.160560
## 2024.1562  -0.4251995674 -36.172393 35.321994 -55.095815 54.245416
## 2024.1589  -0.4265699143 -36.230075 35.376935 -55.183305 54.330165
## 2024.1616  -0.4279402612 -36.287687 35.431806 -55.270690 54.414809
## 2024.1644  -0.4293106081 -36.345230 35.486609 -55.357969 54.499348
## 2024.1671  -0.4306809550 -36.402705 35.541343 -55.445144 54.583782
## 2024.1699  -0.4320513019 -36.460112 35.596009 -55.532215 54.668113
## 2024.1726  -0.4334216489 -36.517451 35.650608 -55.619183 54.752339
## 2024.1753  -0.4347919958 -36.574723 35.705139 -55.706047 54.836463
## 2024.1781  -0.4361623427 -36.631928 35.759603 -55.792808 54.920484
## 2024.1808  -0.4375326896 -36.689065 35.814000 -55.879468 55.004402
## 2024.1836  -0.4389030365 -36.746137 35.868331 -55.966025 55.088219
## 2024.1863  -0.4402733835 -36.803142 35.922595 -56.052482 55.171935
## 2024.1890  -0.4416437304 -36.860081 35.976794 -56.138838 55.255550
## 2024.1918  -0.4430140773 -36.916955 36.030927 -56.225093 55.339065
## 2024.1945  -0.4443844242 -36.973763 36.084995 -56.311249 55.422480
## 2024.1973  -0.4457547711 -37.030507 36.138997 -56.397305 55.505795
## 2024.2000  -0.4471251180 -37.087186 36.192936 -56.483262 55.589012
## 2024.2027  -0.4484954650 -37.143800 36.246809 -56.569121 55.672130
## 2024.2055  -0.4498658119 -37.200351 36.300619 -56.654882 55.755150
## 2024.2082  -0.4512361588 -37.256837 36.354365 -56.740545 55.838073
## 2024.2110  -0.4526065057 -37.313260 36.408047 -56.826112 55.920899
## 2024.2137  -0.4539768526 -37.369620 36.461666 -56.911581 56.003627
## 2024.2164  -0.4553471995 -37.425917 36.515223 -56.996954 56.086260
## 2024.2192  -0.4567175465 -37.482151 36.568716 -57.082232 56.168797
## 2024.2219  -0.4580878934 -37.538323 36.622147 -57.167414 56.251238
## 2024.2247  -0.4594582403 -37.594433 36.675517 -57.252501 56.333585
## 2024.2274  -0.4608285872 -37.650481 36.728824 -57.337494 56.415837
## 2024.2301  -0.4621989341 -37.706468 36.782070 -57.422392 56.497995
## 2024.2329  -0.4635692810 -37.762393 36.835254 -57.507197 56.580059
## 2024.2356  -0.4649396280 -37.818257 36.888378 -57.591909 56.662030
## 2024.2384  -0.4663099749 -37.874061 36.941441 -57.676528 56.743908
## 2024.2411  -0.4676803218 -37.929804 36.994443 -57.761054 56.825693
## 2024.2438  -0.4690506687 -37.985487 37.047385 -57.845488 56.907387
## 2024.2466  -0.4704210156 -38.041110 37.100267 -57.929831 56.988989
## 2024.2493  -0.4717913625 -38.096673 37.153090 -58.014082 57.070499
## 2024.2521  -0.4731617095 -38.152177 37.205853 -58.098242 57.151919
## 2024.2548  -0.4745320564 -38.207622 37.258557 -58.182313 57.233248
## 2024.2575  -0.4759024033 -38.263007 37.311203 -58.266293 57.314488
## 2024.2603  -0.4772727502 -38.318335 37.363789 -58.350183 57.395637
## 2024.2630  -0.4786430971 -38.373604 37.416317 -58.433984 57.476698

print(holt_model$mean)

## Time Series:
## Start = c(2023, 90) 
## End = c(2024, 97) 
## Frequency = 365 
##   [1]  0.0311259561  0.0297556091  0.0283852622  0.0270149153  0.0256445684
##   [6]  0.0242742215  0.0229038746  0.0215335276  0.0201631807  0.0187928338
##  [11]  0.0174224869  0.0160521400  0.0146817931  0.0133114461  0.0119410992
##  [16]  0.0105707523  0.0092004054  0.0078300585  0.0064597116  0.0050893646
##  [21]  0.0037190177  0.0023486708  0.0009783239 -0.0003920230 -0.0017623699
##  [26] -0.0031327169 -0.0045030638 -0.0058734107 -0.0072437576 -0.0086141045
##  [31] -0.0099844515 -0.0113547984 -0.0127251453 -0.0140954922 -0.0154658391
##  [36] -0.0168361860 -0.0182065330 -0.0195768799 -0.0209472268 -0.0223175737
##  [41] -0.0236879206 -0.0250582675 -0.0264286145 -0.0277989614 -0.0291693083
##  [46] -0.0305396552 -0.0319100021 -0.0332803490 -0.0346506960 -0.0360210429
##  [51] -0.0373913898 -0.0387617367 -0.0401320836 -0.0415024305 -0.0428727775
##  [56] -0.0442431244 -0.0456134713 -0.0469838182 -0.0483541651 -0.0497245120
##  [61] -0.0510948590 -0.0524652059 -0.0538355528 -0.0552058997 -0.0565762466
##  [66] -0.0579465936 -0.0593169405 -0.0606872874 -0.0620576343 -0.0634279812
##  [71] -0.0647983281 -0.0661686751 -0.0675390220 -0.0689093689 -0.0702797158
##  [76] -0.0716500627 -0.0730204096 -0.0743907566 -0.0757611035 -0.0771314504
##  [81] -0.0785017973 -0.0798721442 -0.0812424911 -0.0826128381 -0.0839831850
##  [86] -0.0853535319 -0.0867238788 -0.0880942257 -0.0894645726 -0.0908349196
##  [91] -0.0922052665 -0.0935756134 -0.0949459603 -0.0963163072 -0.0976866542
##  [96] -0.0990570011 -0.1004273480 -0.1017976949 -0.1031680418 -0.1045383887
## [101] -0.1059087357 -0.1072790826 -0.1086494295 -0.1100197764 -0.1113901233
## [106] -0.1127604702 -0.1141308172 -0.1155011641 -0.1168715110 -0.1182418579
## [111] -0.1196122048 -0.1209825517 -0.1223528987 -0.1237232456 -0.1250935925
## [116] -0.1264639394 -0.1278342863 -0.1292046332 -0.1305749802 -0.1319453271
## [121] -0.1333156740 -0.1346860209 -0.1360563678 -0.1374267148 -0.1387970617
## [126] -0.1401674086 -0.1415377555 -0.1429081024 -0.1442784493 -0.1456487963
## [131] -0.1470191432 -0.1483894901 -0.1497598370 -0.1511301839 -0.1525005308
## [136] -0.1538708778 -0.1552412247 -0.1566115716 -0.1579819185 -0.1593522654
## [141] -0.1607226123 -0.1620929593 -0.1634633062 -0.1648336531 -0.1662040000
## [146] -0.1675743469 -0.1689446938 -0.1703150408 -0.1716853877 -0.1730557346
## [151] -0.1744260815 -0.1757964284 -0.1771667753 -0.1785371223 -0.1799074692
## [156] -0.1812778161 -0.1826481630 -0.1840185099 -0.1853888569 -0.1867592038
## [161] -0.1881295507 -0.1894998976 -0.1908702445 -0.1922405914 -0.1936109384
## [166] -0.1949812853 -0.1963516322 -0.1977219791 -0.1990923260 -0.2004626729
## [171] -0.2018330199 -0.2032033668 -0.2045737137 -0.2059440606 -0.2073144075
## [176] -0.2086847544 -0.2100551014 -0.2114254483 -0.2127957952 -0.2141661421
## [181] -0.2155364890 -0.2169068359 -0.2182771829 -0.2196475298 -0.2210178767
## [186] -0.2223882236 -0.2237585705 -0.2251289175 -0.2264992644 -0.2278696113
## [191] -0.2292399582 -0.2306103051 -0.2319806520 -0.2333509990 -0.2347213459
## [196] -0.2360916928 -0.2374620397 -0.2388323866 -0.2402027335 -0.2415730805
## [201] -0.2429434274 -0.2443137743 -0.2456841212 -0.2470544681 -0.2484248150
## [206] -0.2497951620 -0.2511655089 -0.2525358558 -0.2539062027 -0.2552765496
## [211] -0.2566468965 -0.2580172435 -0.2593875904 -0.2607579373 -0.2621282842
## [216] -0.2634986311 -0.2648689781 -0.2662393250 -0.2676096719 -0.2689800188
## [221] -0.2703503657 -0.2717207126 -0.2730910596 -0.2744614065 -0.2758317534
## [226] -0.2772021003 -0.2785724472 -0.2799427941 -0.2813131411 -0.2826834880
## [231] -0.2840538349 -0.2854241818 -0.2867945287 -0.2881648756 -0.2895352226
## [236] -0.2909055695 -0.2922759164 -0.2936462633 -0.2950166102 -0.2963869571
## [241] -0.2977573041 -0.2991276510 -0.3004979979 -0.3018683448 -0.3032386917
## [246] -0.3046090386 -0.3059793856 -0.3073497325 -0.3087200794 -0.3100904263
## [251] -0.3114607732 -0.3128311202 -0.3142014671 -0.3155718140 -0.3169421609
## [256] -0.3183125078 -0.3196828547 -0.3210532017 -0.3224235486 -0.3237938955
## [261] -0.3251642424 -0.3265345893 -0.3279049362 -0.3292752832 -0.3306456301
## [266] -0.3320159770 -0.3333863239 -0.3347566708 -0.3361270177 -0.3374973647
## [271] -0.3388677116 -0.3402380585 -0.3416084054 -0.3429787523 -0.3443490992
## [276] -0.3457194462 -0.3470897931 -0.3484601400 -0.3498304869 -0.3512008338
## [281] -0.3525711808 -0.3539415277 -0.3553118746 -0.3566822215 -0.3580525684
## [286] -0.3594229153 -0.3607932623 -0.3621636092 -0.3635339561 -0.3649043030
## [291] -0.3662746499 -0.3676449968 -0.3690153438 -0.3703856907 -0.3717560376
## [296] -0.3731263845 -0.3744967314 -0.3758670783 -0.3772374253 -0.3786077722
## [301] -0.3799781191 -0.3813484660 -0.3827188129 -0.3840891598 -0.3854595068
## [306] -0.3868298537 -0.3882002006 -0.3895705475 -0.3909408944 -0.3923112414
## [311] -0.3936815883 -0.3950519352 -0.3964222821 -0.3977926290 -0.3991629759
## [316] -0.4005333229 -0.4019036698 -0.4032740167 -0.4046443636 -0.4060147105
## [321] -0.4073850574 -0.4087554044 -0.4101257513 -0.4114960982 -0.4128664451
## [326] -0.4142367920 -0.4156071389 -0.4169774859 -0.4183478328 -0.4197181797
## [331] -0.4210885266 -0.4224588735 -0.4238292204 -0.4251995674 -0.4265699143
## [336] -0.4279402612 -0.4293106081 -0.4306809550 -0.4320513019 -0.4334216489
## [341] -0.4347919958 -0.4361623427 -0.4375326896 -0.4389030365 -0.4402733835
## [346] -0.4416437304 -0.4430140773 -0.4443844242 -0.4457547711 -0.4471251180
## [351] -0.4484954650 -0.4498658119 -0.4512361588 -0.4526065057 -0.4539768526
## [356] -0.4553471995 -0.4567175465 -0.4580878934 -0.4594582403 -0.4608285872
## [361] -0.4621989341 -0.4635692810 -0.4649396280 -0.4663099749 -0.4676803218
## [366] -0.4690506687 -0.4704210156 -0.4717913625 -0.4731617095 -0.4745320564
## [371] -0.4759024033 -0.4772727502 -0.4786430971

test_acc_holt <- accuracy(holt_model, x = regular_ts)
print(test_acc_holt)

##                         ME     RMSE       MAE MPE MAPE       MASE      ACF1
## Training set -9.862932e-05 2.695043 1.3098966 NaN  Inf 0.41693248 0.1011700
## Test set      3.015066e-01 0.464242 0.3034368 NaN  Inf 0.09658219 0.2884998
##              Theil's U
## Training set        NA
## Test set           NaN

holt_ts_plot <- autoplot(train) +
  autolayer(holt_model, PI = FALSE, size = 1.1, series = 'Holt Model') +
  autolayer(test, series = 'Test Data')

Regular TS-holt’s damp

holt_damped_model <- holt(train, h = length(test), damped = TRUE)
print(holt_damped_model)

##           Point Forecast      Lo 80     Hi 80      Lo 95     Hi 95
## 2023.2438     0.03383770  -3.429721  3.497397  -5.263218  5.330894
## 2023.2466     0.03382130  -3.911740  3.979383  -6.000394  6.068037
## 2023.2493     0.03380649  -4.341092  4.408705  -6.657024  6.724637
## 2023.2521     0.03379311  -4.732021  4.799608  -7.254891  7.322477
## 2023.2548     0.03378102  -5.093314  5.160877  -7.807435  7.874997
## 2023.2575     0.03377011  -5.430845  5.498385  -8.323637  8.391177
## 2023.2603     0.03376025  -5.748768  5.816289  -8.809854  8.877374
## 2023.2630     0.03375134  -6.050153  6.117656  -9.270778  9.338281
## 2023.2658     0.03374329  -6.337343  6.404829  -9.709992  9.777479
## 2023.2685     0.03373603  -6.612173  6.679645 -10.130305 10.197777
## 2023.2712     0.03372946  -6.876115  6.943574 -10.533965 10.601424
## 2023.2740     0.03372354  -7.130368  7.197816 -10.922810 10.990257
## 2023.2767     0.03371818  -7.375929  7.443365 -11.298359 11.365795
## 2023.2795     0.03371334  -7.613631  7.681058 -11.661890 11.729317
## 2023.2822     0.03370898  -7.844184  7.911602 -12.014488 12.081906
## 2023.2849     0.03370503  -8.068196  8.135606 -12.357083 12.424493
## 2023.2877     0.03370147  -8.286194  8.353597 -12.690480 12.757883
## 2023.2904     0.03369825  -8.498637  8.566034 -13.015383 13.082780
## 2023.2932     0.03369534  -8.705930  8.773321 -13.332409 13.399799
## 2023.2959     0.03369271  -8.908429  8.975815 -13.642103 13.709488
## 2023.2986     0.03369034  -9.106453  9.173833 -13.944952 14.012333
## 2023.3014     0.03368820  -9.300284  9.367660 -14.241390 14.308766
## 2023.3041     0.03368626  -9.490178  9.557551 -14.531807 14.599180
## 2023.3068     0.03368451  -9.676366  9.743735 -14.816556 14.883925
## 2023.3096     0.03368293  -9.859056  9.926421 -15.095955 15.163321
## 2023.3123     0.03368151 -10.038437 10.105800 -15.370295 15.437658
## 2023.3151     0.03368022 -10.214684 10.282045 -15.639841 15.707201
## 2023.3178     0.03367905 -10.387955 10.455313 -15.904835 15.972193
## 2023.3205     0.03367800 -10.558395 10.625751 -16.165500 16.232856
## 2023.3233     0.03367705 -10.726139 10.793493 -16.422041 16.489395
## 2023.3260     0.03367619 -10.891310 10.958662 -16.674648 16.742000
## 2023.3288     0.03367542 -11.054023 11.121374 -16.923496 16.990847
## 2023.3315     0.03367472 -11.214385 11.281735 -17.168748 17.236098
## 2023.3342     0.03367409 -11.372495 11.439843 -17.410556 17.477904
## 2023.3370     0.03367352 -11.528444 11.595791 -17.649060 17.716407
## 2023.3397     0.03367300 -11.682320 11.749666 -17.884392 17.951738
## 2023.3425     0.03367254 -11.834202 11.901547 -18.116675 18.184020
## 2023.3452     0.03367211 -11.984165 12.051510 -18.346024 18.413368
## 2023.3479     0.03367173 -12.132282 12.199625 -18.572549 18.639892
## 2023.3507     0.03367139 -12.278617 12.345960 -18.796350 18.863692
## 2023.3534     0.03367108 -12.423235 12.490577 -19.017523 19.084865
## 2023.3562     0.03367080 -12.566194 12.633535 -19.236159 19.303501
## 2023.3589     0.03367055 -12.707549 12.774890 -19.452344 19.519685
## 2023.3616     0.03367032 -12.847354 12.914695 -19.666157 19.733497
## 2023.3644     0.03367011 -12.985658 13.052999 -19.877675 19.945015
## 2023.3671     0.03366993 -13.122509 13.189849 -20.086970 20.154310
## 2023.3699     0.03366976 -13.257952 13.325291 -20.294111 20.361451
## 2023.3726     0.03366961 -13.392028 13.459368 -20.499164 20.566503
## 2023.3753     0.03366947 -13.524779 13.592118 -20.702189 20.769528
## 2023.3781     0.03366935 -13.656244 13.723582 -20.903246 20.970585
## 2023.3808     0.03366923 -13.786458 13.853796 -21.102391 21.169729
## 2023.3836     0.03366913 -13.915456 13.982795 -21.299677 21.367016
## 2023.3863     0.03366904 -14.043273 14.110611 -21.495156 21.562495
## 2023.3890     0.03366896 -14.169940 14.237278 -21.688877 21.756215
## 2023.3918     0.03366888 -14.295488 14.362825 -21.880885 21.948223
## 2023.3945     0.03366882 -14.419945 14.487282 -22.071226 22.138563
## 2023.3973     0.03366875 -14.543340 14.610677 -22.259942 22.327279
## 2023.4000     0.03366870 -14.665699 14.733036 -22.447073 22.514411
## 2023.4027     0.03366865 -14.787048 14.854385 -22.632661 22.699998
## 2023.4055     0.03366861 -14.907411 14.974748 -22.816741 22.884078
## 2023.4082     0.03366856 -15.026813 15.094150 -22.999350 23.066687
## 2023.4110     0.03366853 -15.145275 15.212612 -23.180523 23.247860
## 2023.4137     0.03366850 -15.262821 15.330158 -23.360293 23.427630
## 2023.4164     0.03366847 -15.379470 15.446806 -23.538692 23.606029
## 2023.4192     0.03366844 -15.495242 15.562579 -23.715751 23.783088
## 2023.4219     0.03366841 -15.610158 15.677495 -23.891500 23.958837
## 2023.4247     0.03366839 -15.724236 15.791573 -24.065967 24.133304
## 2023.4274     0.03366837 -15.837495 15.904831 -24.239181 24.306518
## 2023.4301     0.03366835 -15.949950 16.017287 -24.411167 24.478504
## 2023.4329     0.03366834 -16.061620 16.128957 -24.581952 24.649288
## 2023.4356     0.03366832 -16.172521 16.239858 -24.751560 24.818896
## 2023.4384     0.03366831 -16.282668 16.350005 -24.920015 24.987351
## 2023.4411     0.03366830 -16.392076 16.459413 -25.087340 25.154677
## 2023.4438     0.03366829 -16.500761 16.568097 -25.253559 25.320895
## 2023.4466     0.03366828 -16.608735 16.676072 -25.418692 25.486028
## 2023.4493     0.03366827 -16.716014 16.783351 -25.582760 25.650097
## 2023.4521     0.03366826 -16.822610 16.889947 -25.745785 25.813121
## 2023.4548     0.03366825 -16.928536 16.995873 -25.907785 25.975121
## 2023.4575     0.03366825 -17.033805 17.101141 -26.068779 26.136116
## 2023.4603     0.03366824 -17.138428 17.205765 -26.228787 26.296124
## 2023.4630     0.03366824 -17.242418 17.309755 -26.387826 26.455162
## 2023.4658     0.03366823 -17.345786 17.413122 -26.545913 26.613249
## 2023.4685     0.03366823 -17.448542 17.515879 -26.703065 26.770402
## 2023.4712     0.03366822 -17.550698 17.618035 -26.859299 26.926636
## 2023.4740     0.03366822 -17.652264 17.719601 -27.014631 27.081968
## 2023.4767     0.03366822 -17.753250 17.820587 -27.169076 27.236412
## 2023.4795     0.03366821 -17.853666 17.921003 -27.322649 27.389985
## 2023.4822     0.03366821 -17.953521 18.020858 -27.475364 27.542701
## 2023.4849     0.03366821 -18.052825 18.120162 -27.627237 27.694573
## 2023.4877     0.03366821 -18.151587 18.218924 -27.778280 27.845616
## 2023.4904     0.03366820 -18.249816 18.317152 -27.928507 27.995844
## 2023.4932     0.03366820 -18.347519 18.414855 -28.077932 28.145268
## 2023.4959     0.03366820 -18.444706 18.512042 -28.226566 28.293902
## 2023.4986     0.03366820 -18.541384 18.608720 -28.374423 28.441759
## 2023.5014     0.03366820 -18.637562 18.704898 -28.521514 28.588850
## 2023.5041     0.03366820 -18.733247 18.800583 -28.667851 28.735188
## 2023.5068     0.03366820 -18.828446 18.895783 -28.813446 28.880783
## 2023.5096     0.03366820 -18.923168 18.990504 -28.958310 29.025647
## 2023.5123     0.03366819 -19.017418 19.084754 -29.102454 29.169790
## 2023.5151     0.03366819 -19.111204 19.178541 -29.245888 29.313224
## 2023.5178     0.03366819 -19.204534 19.271870 -29.388623 29.455959
## 2023.5205     0.03366819 -19.297412 19.364749 -29.530668 29.598005
## 2023.5233     0.03366819 -19.389847 19.457183 -29.672035 29.739371
## 2023.5260     0.03366819 -19.481844 19.549180 -29.812732 29.880068
## 2023.5288     0.03366819 -19.573409 19.640745 -29.952768 30.020105
## 2023.5315     0.03366819 -19.664548 19.731885 -30.092154 30.159491
## 2023.5342     0.03366819 -19.755268 19.822604 -30.230898 30.298234
## 2023.5370     0.03366819 -19.845574 19.912910 -30.369009 30.436345
## 2023.5397     0.03366819 -19.935471 20.002807 -30.506495 30.573831
## 2023.5425     0.03366819 -20.024966 20.092302 -30.643365 30.710701
## 2023.5452     0.03366819 -20.114062 20.181399 -30.779627 30.846963
## 2023.5479     0.03366819 -20.202767 20.270104 -30.915289 30.982625
## 2023.5507     0.03366819 -20.291085 20.358421 -31.050359 31.117695
## 2023.5534     0.03366819 -20.379020 20.446356 -31.184845 31.252181
## 2023.5562     0.03366819 -20.466578 20.533915 -31.318753 31.386090
## 2023.5589     0.03366819 -20.553764 20.621101 -31.452093 31.519429
## 2023.5616     0.03366819 -20.640582 20.707919 -31.584869 31.652206
## 2023.5644     0.03366819 -20.727037 20.794374 -31.717091 31.784428
## 2023.5671     0.03366819 -20.813134 20.880470 -31.848764 31.916101
## 2023.5699     0.03366819 -20.898876 20.966213 -31.979896 32.047233
## 2023.5726     0.03366819 -20.984269 21.051606 -32.110493 32.177829
## 2023.5753     0.03366819 -21.069316 21.136653 -32.240561 32.307898
## 2023.5781     0.03366819 -21.154022 21.221358 -32.370108 32.437444
## 2023.5808     0.03366819 -21.238391 21.305727 -32.499138 32.566475
## 2023.5836     0.03366819 -21.322426 21.389762 -32.627659 32.694995
## 2023.5863     0.03366819 -21.406132 21.473468 -32.755676 32.823012
## 2023.5890     0.03366819 -21.489512 21.556848 -32.883195 32.950531
## 2023.5918     0.03366819 -21.572570 21.639907 -33.010222 33.077558
## 2023.5945     0.03366819 -21.655311 21.722647 -33.136763 33.204099
## 2023.5973     0.03366819 -21.737737 21.805073 -33.262822 33.330159
## 2023.6000     0.03366819 -21.819852 21.887188 -33.388406 33.455743
## 2023.6027     0.03366819 -21.901659 21.968996 -33.513520 33.580857
## 2023.6055     0.03366819 -21.983163 22.050499 -33.638170 33.705506
## 2023.6082     0.03366819 -22.064366 22.131703 -33.762359 33.829695
## 2023.6110     0.03366819 -22.145272 22.212608 -33.886094 33.953430
## 2023.6137     0.03366819 -22.225884 22.293220 -34.009379 34.076715
## 2023.6164     0.03366819 -22.306205 22.373541 -34.132219 34.199555
## 2023.6192     0.03366819 -22.386238 22.453574 -34.254619 34.321955
## 2023.6219     0.03366819 -22.465986 22.533322 -34.376584 34.443920
## 2023.6247     0.03366819 -22.545453 22.612789 -34.498118 34.565454
## 2023.6274     0.03366819 -22.624641 22.691977 -34.619225 34.686562
## 2023.6301     0.03366819 -22.703553 22.770890 -34.739911 34.807248
## 2023.6329     0.03366819 -22.782193 22.849529 -34.860180 34.927516
## 2023.6356     0.03366819 -22.860562 22.927898 -34.980035 35.047371
## 2023.6384     0.03366819 -22.938664 23.006000 -35.099481 35.166818
## 2023.6411     0.03366819 -23.016501 23.083837 -35.218523 35.285860
## 2023.6438     0.03366819 -23.094076 23.161412 -35.337164 35.404501
## 2023.6466     0.03366819 -23.171392 23.238728 -35.455409 35.522745
## 2023.6493     0.03366819 -23.248451 23.315788 -35.573261 35.640597
## 2023.6521     0.03366819 -23.325256 23.392593 -35.690724 35.758060
## 2023.6548     0.03366819 -23.401809 23.469146 -35.807802 35.875138
## 2023.6575     0.03366819 -23.478113 23.545450 -35.924499 35.991835
## 2023.6603     0.03366819 -23.554171 23.621507 -36.040818 36.108155
## 2023.6630     0.03366819 -23.629983 23.697320 -36.156764 36.224100
## 2023.6658     0.03366819 -23.705554 23.772890 -36.272339 36.339675
## 2023.6685     0.03366819 -23.780885 23.848221 -36.387548 36.454884
## 2023.6712     0.03366819 -23.855978 23.923314 -36.502393 36.569729
## 2023.6740     0.03366819 -23.930836 23.998172 -36.616878 36.684215
## 2023.6767     0.03366819 -24.005461 24.072797 -36.731007 36.798343
## 2023.6795     0.03366819 -24.079855 24.147191 -36.844783 36.912119
## 2023.6822     0.03366819 -24.154020 24.221356 -36.958209 37.025545
## 2023.6849     0.03366819 -24.227958 24.295295 -37.071288 37.138624
## 2023.6877     0.03366819 -24.301672 24.369008 -37.184023 37.251359
## 2023.6904     0.03366819 -24.375163 24.442500 -37.296418 37.363754
## 2023.6932     0.03366819 -24.448434 24.515770 -37.408476 37.475812
## 2023.6959     0.03366819 -24.521486 24.588822 -37.520199 37.587535
## 2023.6986     0.03366819 -24.594321 24.661657 -37.631591 37.698927
## 2023.7014     0.03366819 -24.666941 24.734278 -37.742654 37.809990
## 2023.7041     0.03366819 -24.739349 24.806685 -37.853392 37.920728
## 2023.7068     0.03366819 -24.811545 24.878882 -37.963807 38.031143
## 2023.7096     0.03366819 -24.883533 24.950869 -38.073902 38.141238
## 2023.7123     0.03366819 -24.955313 25.022649 -38.183680 38.251016
## 2023.7151     0.03366819 -25.026887 25.094223 -38.293143 38.360480
## 2023.7178     0.03366819 -25.098257 25.165594 -38.402295 38.469632
## 2023.7205     0.03366819 -25.169426 25.236762 -38.511138 38.578474
## 2023.7233     0.03366819 -25.240394 25.307730 -38.619674 38.687011
## 2023.7260     0.03366819 -25.311163 25.378500 -38.727907 38.795243
## 2023.7288     0.03366819 -25.381735 25.449072 -38.835838 38.903174
## 2023.7315     0.03366819 -25.452112 25.519449 -38.943470 39.010806
## 2023.7342     0.03366819 -25.522295 25.589632 -39.050805 39.118142
## 2023.7370     0.03366819 -25.592286 25.659623 -39.157847 39.225183
## 2023.7397     0.03366819 -25.662086 25.729423 -39.264597 39.331933
## 2023.7425     0.03366819 -25.731697 25.799034 -39.371058 39.438394
## 2023.7452     0.03366819 -25.801121 25.868457 -39.477232 39.544569
## 2023.7479     0.03366819 -25.870358 25.937695 -39.583122 39.650458
## 2023.7507     0.03366819 -25.939411 26.006748 -39.688729 39.756065
## 2023.7534     0.03366819 -26.008281 26.075617 -39.794056 39.861393
## 2023.7562     0.03366819 -26.076969 26.144306 -39.899106 39.966442
## 2023.7589     0.03366819 -26.145477 26.212814 -40.003880 40.071216
## 2023.7616     0.03366819 -26.213806 26.281143 -40.108380 40.175716
## 2023.7644     0.03366819 -26.281958 26.349294 -40.212609 40.279945
## 2023.7671     0.03366819 -26.349934 26.417270 -40.316569 40.383905
## 2023.7699     0.03366819 -26.417735 26.485071 -40.420261 40.487598
## 2023.7726     0.03366819 -26.485362 26.552699 -40.523689 40.591025
## 2023.7753     0.03366819 -26.552818 26.620154 -40.626853 40.694190
## 2023.7781     0.03366819 -26.620103 26.687439 -40.729757 40.797093
## 2023.7808     0.03366819 -26.687218 26.754554 -40.832401 40.899737
## 2023.7836     0.03366819 -26.754165 26.821502 -40.934788 41.002124
## 2023.7863     0.03366819 -26.820946 26.888282 -41.036920 41.104256
## 2023.7890     0.03366819 -26.887561 26.954897 -41.138798 41.206135
## 2023.7918     0.03366819 -26.954011 27.021347 -41.240425 41.307762
## 2023.7945     0.03366819 -27.020298 27.087634 -41.341803 41.409139
## 2023.7973     0.03366819 -27.086423 27.153759 -41.442932 41.510268
## 2023.8000     0.03366819 -27.152387 27.219724 -41.543816 41.611152
## 2023.8027     0.03366819 -27.218192 27.285528 -41.644455 41.711792
## 2023.8055     0.03366819 -27.283838 27.351174 -41.744852 41.812188
## 2023.8082     0.03366819 -27.349327 27.416663 -41.845008 41.912345
## 2023.8110     0.03366819 -27.414659 27.481995 -41.944926 42.012262
## 2023.8137     0.03366819 -27.479836 27.547173 -42.044606 42.111942
## 2023.8164     0.03366819 -27.544860 27.612196 -42.144050 42.211387
## 2023.8192     0.03366819 -27.609730 27.677066 -42.243261 42.310597
## 2023.8219     0.03366819 -27.674448 27.741785 -42.342239 42.409576
## 2023.8247     0.03366819 -27.739016 27.806352 -42.440987 42.508323
## 2023.8274     0.03366819 -27.803434 27.870770 -42.539506 42.606842
## 2023.8301     0.03366819 -27.867703 27.935039 -42.637797 42.705133
## 2023.8329     0.03366819 -27.931824 27.999161 -42.735862 42.803198
## 2023.8356     0.03366819 -27.995799 28.063136 -42.833703 42.901039
## 2023.8384     0.03366819 -28.059628 28.126965 -42.931321 42.998658
## 2023.8411     0.03366819 -28.123313 28.190649 -43.028718 43.096054
## 2023.8438     0.03366819 -28.186853 28.254190 -43.125895 43.193231
## 2023.8466     0.03366819 -28.250251 28.317588 -43.222854 43.290190
## 2023.8493     0.03366819 -28.313507 28.380844 -43.319596 43.386932
## 2023.8521     0.03366819 -28.376623 28.443959 -43.416122 43.483459
## 2023.8548     0.03366819 -28.439598 28.506934 -43.512435 43.579771
## 2023.8575     0.03366819 -28.502435 28.569771 -43.608535 43.675871
## 2023.8603     0.03366819 -28.565133 28.632469 -43.704424 43.771760
## 2023.8630     0.03366819 -28.627694 28.695030 -43.800103 43.867439
## 2023.8658     0.03366819 -28.690119 28.757455 -43.895573 43.962910
## 2023.8685     0.03366819 -28.752409 28.819745 -43.990837 44.058173
## 2023.8712     0.03366819 -28.814564 28.881900 -44.085895 44.153231
## 2023.8740     0.03366819 -28.876585 28.943921 -44.180749 44.248085
## 2023.8767     0.03366819 -28.938474 29.005810 -44.275399 44.342736
## 2023.8795     0.03366819 -29.000230 29.067567 -44.369848 44.437184
## 2023.8822     0.03366819 -29.061856 29.129192 -44.464096 44.531433
## 2023.8849     0.03366819 -29.123352 29.190688 -44.558145 44.625482
## 2023.8877     0.03366819 -29.184718 29.252054 -44.651997 44.719333
## 2023.8904     0.03366819 -29.245955 29.313291 -44.745651 44.812987
## 2023.8932     0.03366819 -29.307064 29.374401 -44.839110 44.906446
## 2023.8959     0.03366819 -29.368047 29.435383 -44.932375 44.999711
## 2023.8986     0.03366819 -29.428903 29.496240 -45.025447 45.092783
## 2023.9014     0.03366819 -29.489634 29.556971 -45.118326 45.185663
## 2023.9041     0.03366819 -29.550240 29.617577 -45.211016 45.278352
## 2023.9068     0.03366819 -29.610723 29.678059 -45.303515 45.370852
## 2023.9096     0.03366819 -29.671082 29.738418 -45.395827 45.463163
## 2023.9123     0.03366819 -29.731319 29.798655 -45.487951 45.555287
## 2023.9151     0.03366819 -29.791434 29.858770 -45.579889 45.647225
## 2023.9178     0.03366819 -29.851428 29.918764 -45.671642 45.738979
## 2023.9205     0.03366819 -29.911302 29.978638 -45.763211 45.830548
## 2023.9233     0.03366819 -29.971056 30.038393 -45.854598 45.921934
## 2023.9260     0.03366819 -30.030692 30.098028 -45.945803 46.013139
## 2023.9288     0.03366819 -30.090210 30.157546 -46.036828 46.104164
## 2023.9315     0.03366819 -30.149610 30.216946 -46.127672 46.195009
## 2023.9342     0.03366819 -30.208894 30.276230 -46.218339 46.285675
## 2023.9370     0.03366819 -30.268061 30.335398 -46.308828 46.376164
## 2023.9397     0.03366819 -30.327114 30.394450 -46.399141 46.466477
## 2023.9425     0.03366819 -30.386051 30.453388 -46.489278 46.556615
## 2023.9452     0.03366819 -30.444875 30.512212 -46.579242 46.646578
## 2023.9479     0.03366819 -30.503586 30.570922 -46.669031 46.736368
## 2023.9507     0.03366819 -30.562183 30.629520 -46.758649 46.825985
## 2023.9534     0.03366819 -30.620669 30.688006 -46.848095 46.915432
## 2023.9562     0.03366819 -30.679044 30.746380 -46.937371 47.004708
## 2023.9589     0.03366819 -30.737307 30.804644 -47.026478 47.093814
## 2023.9616     0.03366819 -30.795461 30.862797 -47.115416 47.182752
## 2023.9644     0.03366819 -30.853505 30.920841 -47.204187 47.271523
## 2023.9671     0.03366819 -30.911440 30.978776 -47.292791 47.360127
## 2023.9699     0.03366819 -30.969267 31.036603 -47.381229 47.448566
## 2023.9726     0.03366819 -31.026986 31.094323 -47.469503 47.536840
## 2023.9753     0.03366819 -31.084598 31.151935 -47.557614 47.624950
## 2023.9781     0.03366819 -31.142104 31.209440 -47.645561 47.712897
## 2023.9808     0.03366819 -31.199504 31.266840 -47.733347 47.800683
## 2023.9836     0.03366819 -31.256799 31.324135 -47.820971 47.888307
## 2023.9863     0.03366819 -31.313988 31.381325 -47.908435 47.975772
## 2023.9890     0.03366819 -31.371074 31.438410 -47.995740 48.063077
## 2023.9918     0.03366819 -31.428056 31.495393 -48.082887 48.150223
## 2023.9945     0.03366819 -31.484935 31.552272 -48.169876 48.237212
## 2023.9973     0.03366819 -31.541712 31.609048 -48.256708 48.324045
## 2024.0000     0.03366819 -31.598387 31.665723 -48.343385 48.410721
## 2024.0027     0.03366819 -31.654960 31.722296 -48.429906 48.497243
## 2024.0055     0.03366819 -31.711433 31.778769 -48.516274 48.583610
## 2024.0082     0.03366819 -31.767805 31.835141 -48.602488 48.669824
## 2024.0110     0.03366819 -31.824077 31.891414 -48.688549 48.755885
## 2024.0137     0.03366819 -31.880251 31.947587 -48.774459 48.841795
## 2024.0164     0.03366819 -31.936325 32.003662 -48.860217 48.927554
## 2024.0192     0.03366819 -31.992302 32.059638 -48.945826 49.013162
## 2024.0219     0.03366819 -32.048180 32.115517 -49.031285 49.098621
## 2024.0247     0.03366819 -32.103962 32.171298 -49.116596 49.183932
## 2024.0274     0.03366819 -32.159647 32.226983 -49.201758 49.269095
## 2024.0301     0.03366819 -32.215236 32.282572 -49.286774 49.354110
## 2024.0329     0.03366819 -32.270729 32.338065 -49.371643 49.438980
## 2024.0356     0.03366819 -32.326127 32.393463 -49.456367 49.523704
## 2024.0384     0.03366819 -32.381430 32.448766 -49.540946 49.608283
## 2024.0411     0.03366819 -32.436639 32.503975 -49.625381 49.692718
## 2024.0438     0.03366819 -32.491754 32.559091 -49.709673 49.777010
## 2024.0466     0.03366819 -32.546777 32.614113 -49.793822 49.861159
## 2024.0493     0.03366819 -32.601706 32.669042 -49.877829 49.945166
## 2024.0521     0.03366819 -32.656543 32.723879 -49.961696 50.029032
## 2024.0548     0.03366819 -32.711288 32.778625 -50.045421 50.112758
## 2024.0575     0.03366819 -32.765942 32.833279 -50.129007 50.196343
## 2024.0603     0.03366819 -32.820505 32.887841 -50.212454 50.279790
## 2024.0630     0.03366819 -32.874978 32.942314 -50.295762 50.363099
## 2024.0658     0.03366819 -32.929360 32.996696 -50.378933 50.446270
## 2024.0685     0.03366819 -32.983653 33.050989 -50.461967 50.529303
## 2024.0712     0.03366819 -33.037857 33.105193 -50.544864 50.612201
## 2024.0740     0.03366819 -33.091972 33.159308 -50.627626 50.694963
## 2024.0767     0.03366819 -33.145999 33.213335 -50.710253 50.777590
## 2024.0795     0.03366819 -33.199938 33.267274 -50.792746 50.860082
## 2024.0822     0.03366819 -33.253789 33.321126 -50.875105 50.942441
## 2024.0849     0.03366819 -33.307554 33.374890 -50.957330 51.024667
## 2024.0877     0.03366819 -33.361232 33.428568 -51.039424 51.106760
## 2024.0904     0.03366819 -33.414824 33.482160 -51.121386 51.188722
## 2024.0932     0.03366819 -33.468330 33.535666 -51.203216 51.270553
## 2024.0959     0.03366819 -33.521751 33.589087 -51.284916 51.352253
## 2024.0986     0.03366819 -33.575087 33.642423 -51.366487 51.433823
## 2024.1014     0.03366819 -33.628338 33.695674 -51.447928 51.515264
## 2024.1041     0.03366819 -33.681505 33.748842 -51.529240 51.596577
## 2024.1068     0.03366819 -33.734589 33.801925 -51.610425 51.677761
## 2024.1096     0.03366819 -33.787589 33.854926 -51.691481 51.758818
## 2024.1123     0.03366819 -33.840507 33.907843 -51.772412 51.839748
## 2024.1151     0.03366819 -33.893341 33.960678 -51.853216 51.920552
## 2024.1178     0.03366819 -33.946094 34.013431 -51.933894 52.001230
## 2024.1205     0.03366819 -33.998765 34.066101 -52.014447 52.081783
## 2024.1233     0.03366819 -34.051355 34.118691 -52.094876 52.162212
## 2024.1260     0.03366819 -34.103863 34.171199 -52.175181 52.242517
## 2024.1288     0.03366819 -34.156291 34.223627 -52.255362 52.322698
## 2024.1315     0.03366819 -34.208639 34.275975 -52.335421 52.402757
## 2024.1342     0.03366819 -34.260906 34.328243 -52.415357 52.482694
## 2024.1370     0.03366819 -34.313094 34.380431 -52.495172 52.562509
## 2024.1397     0.03366819 -34.365203 34.432540 -52.574866 52.642202
## 2024.1425     0.03366819 -34.417233 34.484570 -52.654439 52.721776
## 2024.1452     0.03366819 -34.469185 34.536522 -52.733892 52.801229
## 2024.1479     0.03366819 -34.521059 34.588395 -52.813226 52.880563
## 2024.1507     0.03366819 -34.572855 34.640191 -52.892441 52.959778
## 2024.1534     0.03366819 -34.624573 34.691909 -52.971538 53.038874
## 2024.1562     0.03366819 -34.676214 34.743551 -53.050516 53.117853
## 2024.1589     0.03366819 -34.727779 34.795115 -53.129378 53.196714
## 2024.1616     0.03366819 -34.779267 34.846604 -53.208122 53.275458
## 2024.1644     0.03366819 -34.830679 34.898016 -53.286750 53.354087
## 2024.1671     0.03366819 -34.882016 34.949352 -53.365263 53.432599
## 2024.1699     0.03366819 -34.933277 35.000614 -53.443660 53.510996
## 2024.1726     0.03366819 -34.984463 35.051800 -53.521942 53.589279
## 2024.1753     0.03366819 -35.035575 35.102911 -53.600110 53.667447
## 2024.1781     0.03366819 -35.086612 35.153948 -53.678165 53.745501
## 2024.1808     0.03366819 -35.137575 35.204911 -53.756106 53.823442
## 2024.1836     0.03366819 -35.188464 35.255800 -53.833934 53.901271
## 2024.1863     0.03366819 -35.239280 35.306616 -53.911650 53.978987
## 2024.1890     0.03366819 -35.290022 35.357359 -53.989255 54.056591
## 2024.1918     0.03366819 -35.340692 35.408029 -54.066748 54.134084
## 2024.1945     0.03366819 -35.391290 35.458626 -54.144130 54.211466
## 2024.1973     0.03366819 -35.441815 35.509151 -54.221401 54.288738
## 2024.2000     0.03366819 -35.492268 35.559605 -54.298563 54.365900
## 2024.2027     0.03366819 -35.542650 35.609987 -54.375616 54.442952
## 2024.2055     0.03366819 -35.592961 35.660297 -54.452559 54.519895
## 2024.2082     0.03366819 -35.643201 35.710537 -54.529394 54.596730
## 2024.2110     0.03366819 -35.693370 35.760706 -54.606121 54.673457
## 2024.2137     0.03366819 -35.743468 35.810805 -54.682740 54.750077
## 2024.2164     0.03366819 -35.793497 35.860833 -54.759252 54.826589
## 2024.2192     0.03366819 -35.843456 35.910792 -54.835658 54.902994
## 2024.2219     0.03366819 -35.893345 35.960681 -54.911957 54.979294
## 2024.2247     0.03366819 -35.943165 36.010502 -54.988151 55.055487
## 2024.2274     0.03366819 -35.992917 36.060253 -55.064239 55.131575
## 2024.2301     0.03366819 -36.042599 36.109936 -55.140222 55.207558
## 2024.2329     0.03366819 -36.092214 36.159550 -55.216100 55.283437
## 2024.2356     0.03366819 -36.141760 36.209096 -55.291875 55.359211
## 2024.2384     0.03366819 -36.191239 36.258575 -55.367546 55.434882
## 2024.2411     0.03366819 -36.240650 36.307986 -55.443114 55.510450
## 2024.2438     0.03366819 -36.289993 36.357330 -55.518578 55.585915
## 2024.2466     0.03366819 -36.339270 36.406607 -55.593941 55.661277
## 2024.2493     0.03366819 -36.388481 36.455817 -55.669202 55.736538
## 2024.2521     0.03366819 -36.437625 36.504961 -55.744361 55.811697
## 2024.2548     0.03366819 -36.486702 36.554039 -55.819419 55.886755
## 2024.2575     0.03366819 -36.535714 36.603050 -55.894376 55.961712
## 2024.2603     0.03366819 -36.584660 36.651997 -55.969232 56.036569
## 2024.2630     0.03366819 -36.633541 36.700878 -56.043989 56.111326

print(holt_damped_model$mean)

## Time Series:
## Start = c(2023, 90) 
## End = c(2024, 97) 
## Frequency = 365 
##   [1] 0.03383770 0.03382130 0.03380649 0.03379311 0.03378102 0.03377011
##   [7] 0.03376025 0.03375134 0.03374329 0.03373603 0.03372946 0.03372354
##  [13] 0.03371818 0.03371334 0.03370898 0.03370503 0.03370147 0.03369825
##  [19] 0.03369534 0.03369271 0.03369034 0.03368820 0.03368626 0.03368451
##  [25] 0.03368293 0.03368151 0.03368022 0.03367905 0.03367800 0.03367705
##  [31] 0.03367619 0.03367542 0.03367472 0.03367409 0.03367352 0.03367300
##  [37] 0.03367254 0.03367211 0.03367173 0.03367139 0.03367108 0.03367080
##  [43] 0.03367055 0.03367032 0.03367011 0.03366993 0.03366976 0.03366961
##  [49] 0.03366947 0.03366935 0.03366923 0.03366913 0.03366904 0.03366896
##  [55] 0.03366888 0.03366882 0.03366875 0.03366870 0.03366865 0.03366861
##  [61] 0.03366856 0.03366853 0.03366850 0.03366847 0.03366844 0.03366841
##  [67] 0.03366839 0.03366837 0.03366835 0.03366834 0.03366832 0.03366831
##  [73] 0.03366830 0.03366829 0.03366828 0.03366827 0.03366826 0.03366825
##  [79] 0.03366825 0.03366824 0.03366824 0.03366823 0.03366823 0.03366822
##  [85] 0.03366822 0.03366822 0.03366821 0.03366821 0.03366821 0.03366821
##  [91] 0.03366820 0.03366820 0.03366820 0.03366820 0.03366820 0.03366820
##  [97] 0.03366820 0.03366820 0.03366819 0.03366819 0.03366819 0.03366819
## [103] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [109] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [115] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [121] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [127] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [133] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [139] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [145] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [151] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [157] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [163] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [169] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [175] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [181] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [187] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [193] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [199] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [205] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [211] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [217] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [223] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [229] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [235] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [241] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [247] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [253] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [259] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [265] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [271] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [277] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [283] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [289] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [295] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [301] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [307] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [313] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [319] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [325] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [331] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [337] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [343] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [349] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [355] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [361] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [367] 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819 0.03366819
## [373] 0.03366819

test_acc_holtd <- accuracy(holt_damped_model, x = regular_ts)

holt_damped_ts_plot <- autoplot(train) +
  autolayer(holt_damped_model, PI = FALSE, size = 1.1, series = "Holt's Damped Model") +
  autolayer(test, series = 'Test Data')

Regular TS-arima (model could not be performed because of data constraints)

lambda <- BoxCox.lambda(train)

## Warning in guerrero(x, lower, upper): Guerrero's method for selecting a Box-Cox
## parameter (lambda) is given for strictly positive data.

ts_const_var <- BoxCox(train, lambda = lambda)

autoplot(ts_const_var)

ts_const_var_no_seasonality <- diff(x = ts_const_var, lag = 12)
autoplot(ts_const_var_no_seasonality)

dat <- cbind(original = train,
             const_var = ts_const_var,
             no_seasonality = ts_const_var_no_seasonality)

autoplot(dat, facets = TRUE, colour = TRUE) + 
    ylab('') + 
    xlab('Year') + 
    theme_bw()

ggAcf(train)

ggAcf(ts_const_var_no_seasonality)

kpss_result <- kpss.test(ts_const_var_no_seasonality)

## Warning in kpss.test(ts_const_var_no_seasonality): p-value greater than printed
## p-value

print(kpss_result)

## 
##  KPSS Test for Level Stationarity
## 
## data:  ts_const_var_no_seasonality
## KPSS Level = 0.059689, Truncation lag parameter = 6, p-value = 0.1

Regular TS- lags

ts_const_var_no_seasonality_no_trend <- diff(ts_const_var_no_seasonality, 1)
autoplot(ts_const_var_no_seasonality_no_trend)

dat <- cbind(orig = train,
             const_var = ts_const_var,
             no_season = ts_const_var_no_seasonality,
             no_trend = ts_const_var_no_seasonality_no_trend)

autoplot(dat, colour = TRUE, facets = TRUE) + 
    xlab('Year') + 
    ylab('') + 
    theme_bw()

kpss_result_no_trend <- kpss.test(ts_const_var_no_seasonality_no_trend)

## Warning in kpss.test(ts_const_var_no_seasonality_no_trend): p-value greater
## than printed p-value

print(kpss_result_no_trend)

## 
##  KPSS Test for Level Stationarity
## 
## data:  ts_const_var_no_seasonality_no_trend
## KPSS Level = 0.0060968, Truncation lag parameter = 6, p-value = 0.1

####Bi-Weekly

library(zoo)
library(lubridate)

start_time <- start(regular_ts)
frequency <- frequency(regular_ts)

start_date <- if (frequency == 365) {
  as.Date(paste(start_time[1], "1", "1", sep = "-")) + (start_time[2] - 1)
} else {
  stop("The time series does not have a daily frequency.")
}

dates <- seq(from = start_date, by = "day", length.out = length(regular_ts))

zoo_obj <- zoo(regular_ts, order.by = dates)

bi_monthly_data <- aggregate(zoo_obj, by = function(time) {
  year <- format(time, "%Y")
  two_month_period <- ceiling(as.numeric(format(time, "%m")) / 2)
  paste(year, two_month_period, sep = "-")
}, FUN = sum)

regular_ts_bi_monthly <- ts(coredata(bi_monthly_data), start = c(start_time[1], ceiling(as.numeric(format(start_date, "%m")) / 2)), frequency = 6)

train_end_index_week <- round(length(regular_ts_bi_monthly) * 0.7)

ts_start_week <- start(regular_ts_bi_monthly)
ts_frequency_week <- frequency(regular_ts_bi_monthly)

train_week <- window(regular_ts_bi_monthly, end = ts_start_week + (train_end_index_week - 1)/ts_frequency_week)
test_week <- window(regular_ts_bi_monthly, start = ts_start_week + train_end_index_week/ts_frequency_week)

length(train_week)

## [1] 17

start(train_week)

## [1] 2020    5

end(train_week)

## [1] 2023    3

length(test_week)

## [1] 4

start(test_week)

## [1] 2023    5

end(test_week)

## [1] 2024    2

####Bi-Weekly-holt’s winter additive

hw_additive <- hw(train_week, h = length(test_week), seasonal = 'additive', damped = TRUE)

print(hw_additive$mean)

## Time Series:
## Start = c(2023, 4) 
## End = c(2024, 1) 
## Frequency = 6 
## [1] -60.67278 -34.28602 -65.86971 -64.53150

test_acc_holta <- accuracy(hw_additive, x = regular_ts_bi_monthly)
print(test_acc_holta)

##                     ME     RMSE      MAE        MPE     MAPE      MASE
## Training set -11.11768 91.36842 63.75159  -31.06237 2487.833 0.5444624
## Test set      62.09000 64.00371 62.09000 1416.09321 1416.093 0.5302718
##                    ACF1 Theil's U
## Training set -0.1320466        NA
## Test set     -0.1803783   15.4203

####Bi-Weekly-holt’s winter multi

hw_multiplicative <- hw(train_week, h = length(test_week), seasonal = 'multiplicative', damped = TRUE)

print(hw_multiplicative$mean)

## Time Series:
## Start = c(2023, 4) 
## End = c(2024, 1) 
## Frequency = 6 
## [1]  5.480349  6.751522  3.578859 -0.496982

test_acc_holtm <- accuracy(hw_multiplicative, x = regular_ts_bi_monthly)
print(test_acc_holtm)

##                      ME     RMSE       MAE         MPE      MAPE      MASE
## Training set -14.912900 68.29210 51.567988 -1253.39072 1280.7118 0.4404098
## Test set       1.921563  6.56913  5.537498   -41.71573  118.4115 0.0472923
##                   ACF1 Theil's U
## Training set 0.3047552        NA
## Test set     0.2136701  1.102724

####Bi-Weekly-ets-aaa

ets_aaa <- ets(train_week, model = 'AAA')

print(coef(ets_aaa))

##         alpha          beta         gamma             l             b 
##  1.001135e-04  1.000113e-04  9.998998e-01  2.390264e+02 -1.601424e+01 
##            s0            s1            s2            s3            s4 
## -4.700998e+01  3.086967e+01 -5.129327e+01  3.795717e+01  3.299301e+02

print(summary(ets_aaa))

## ETS(A,A,A) 
## 
## Call:
##  ets(y = train_week, model = "AAA") 
## 
##   Smoothing parameters:
##     alpha = 1e-04 
##     beta  = 1e-04 
##     gamma = 0.9999 
## 
##   Initial states:
##     l = 239.0264 
##     b = -16.0142 
##     s = -47.01 30.8697 -51.2933 37.9572 329.9301 -300.4537
## 
##   sigma:  140.6187
## 
##      AIC     AICc      BIC 
## 223.2462 276.0462 232.4116 
## 
## Training set error measures:
##                     ME     RMSE      MAE      MPE     MAPE      MASE      ACF1
## Training set 0.5855768 90.23349 64.84454 417.6511 2655.054 0.5537965 -0.146081

checkresiduals(ets_aaa)

## 
##  Ljung-Box test
## 
## data:  Residuals from ETS(A,A,A)
## Q* = 1.1548, df = 3, p-value = 0.7639
## 
## Model df: 0.   Total lags used: 3

ets_aaa_forecast <- forecast(ets_aaa, h = length(test_week))
print(ets_aaa_forecast)

##          Point Forecast     Lo 80     Hi 80     Lo 95    Hi 95
## 2023.500      -87.13381 -267.3440  93.07635 -362.7415 188.4738
## 2023.667      -62.12735 -242.3375 118.08281 -337.7350 213.4803
## 2023.833      -95.10316 -275.3133  85.10701 -370.7108 180.5045
## 2024.000      -95.08737 -275.2975  85.12282 -370.6951 180.5203

test_acc_aaa <- accuracy(ets_aaa_forecast, x = regular_ts_bi_monthly)
print(test_acc_aaa)

##                      ME     RMSE      MAE       MPE     MAPE      MASE
## Training set  0.5855768 90.23349 64.84454  417.6511 2655.054 0.5537965
## Test set     90.6129218 92.08149 90.61292 2158.4688 2158.469 0.7738681
##                    ACF1 Theil's U
## Training set -0.1460810        NA
## Test set     -0.1060668  22.18968

checkresiduals(ets_aaa)

## 
##  Ljung-Box test
## 
## data:  Residuals from ETS(A,A,A)
## Q* = 1.1548, df = 3, p-value = 0.7639
## 
## Model df: 0.   Total lags used: 3

####Bi-Weekly-ets:auto

ets_auto <- ets(train_week)

summary(ets_auto)

## ETS(M,N,N) 
## 
## Call:
##  ets(y = train_week) 
## 
##   Smoothing parameters:
##     alpha = 0.6811 
## 
##   Initial states:
##     l = 865.6953 
## 
##   sigma:  0.9139
## 
##      AIC     AICc      BIC 
## 192.4424 194.2886 194.9420 
## 
## Training set error measures:
##                     ME    RMSE      MAE       MPE     MAPE     MASE       ACF1
## Training set -74.58086 240.577 129.2276 -5443.801 5467.523 1.103652 -0.3438506

ets_auto_forecast <- forecast(ets_auto, h = length(test_week))
print(ets_auto_forecast)

##          Point Forecast      Lo 80    Hi 80     Lo 95     Hi 95
## 2023.500        2.14456 -0.3670685 4.656189 -1.696645  5.985765
## 2023.667        2.14456 -1.2728441 5.561965 -3.081909  7.371029
## 2023.833        2.14456 -2.2291831 6.518304 -4.544503  8.833624
## 2024.000        2.14456 -3.2838179 7.572939 -6.157428 10.446549

test_acc_auto <- accuracy(ets_auto_forecast, x = regular_ts_bi_monthly)
print(test_acc_auto)

##                     ME       RMSE       MAE         MPE       MAPE      MASE
## Training set -74.58086 240.576981 129.22762 -5443.80126 5467.52323 1.1036520
## Test set       3.60544   5.068204   3.67772    42.78851   46.40252 0.0314091
##                    ACF1 Theil's U
## Training set -0.3438506        NA
## Test set      0.2401478   1.05875

ets_forecast_plot <- autoplot(ets_auto_forecast) +
  autolayer(train_week, series = 'Training Data') +
  autolayer(test_week, series = 'Test Data') +
  ggtitle('ETS Model Forecast vs Actuals') +
  xlab('Time') + ylab('Values') +
  labs(colour = 'Series') +
  theme_minimal()

C. Character Revenue Analysis

Prior to commencing regression analysis, it is important to address a prevailing issue. The rev data set contains a significant amount of character variables, each of which has multiple unique classifications. When conducting regression analysis on all variables, MLR will automatically apply one-hot encoding to all categorical variables. This will greatly augment the complexity of the data and give rise to the “curse of dimensionality,” which refers to the scenario when there are more explanatory factors than observations, leading to issues with multicollinearity and model overfitting. Hence, it is imperative to perform feature selection before conducting regression analysis. Utilizing our extensive knowledge in the field and employing a systematic approach, we have identified seven explanatory factors for regression analysis: base_atk, rerun, special_2, talent_weekly, special_6, release_year, and size.

##Feature selection##

#Exclude variables based on domain knowledge
rev1 <- rev %>% 
  select(-id, -character_name, -rarity, -voice_eng, -voice_cn, -voice_jp, -voice_kr, 
         -special_dish, -talent_material, -talent_book_1.2, -talent_book_2.3,
         -talent_book_3.4, -talent_book_4.5, -talent_book_5.6, -talent_book_6.7,
         -talent_book_7.8,-talent_book_8.9)

start_mod = lm(revenue~1, data = rev1)
empty_mod = lm(revenue~1, data = rev1)
full_mod = lm(revenue~., data = rev1)
hybridStepwise = step(start_mod, scope = list(upper = full_mod, lower = empty_mod), direction = "both");

## Start:  AIC=1589.21
## revenue ~ 1
## 
##                       Df  Sum of Sq        RSS    AIC
## + base_atk             1 1.4254e+14 2.9143e+15 1588.8
## + special_3            1 1.3815e+14 2.9187e+15 1588.9
## + special_4            1 1.3815e+14 2.9187e+15 1588.9
## + special_6            1 1.3804e+14 2.9188e+15 1588.9
## + special_5            1 1.3781e+14 2.9190e+15 1588.9
## + special_2            1 1.3715e+14 2.9197e+15 1588.9
## + release_year         1 1.2865e+14 2.9282e+15 1589.1
## + max_lv_atk           1 1.2020e+14 2.9366e+15 1589.2
## <none>                              3.0568e+15 1589.2
## + gender               1 1.1726e+14 2.9396e+15 1589.2
## + max_ascencion_atk    1 1.0443e+14 2.9524e+15 1589.5
## + base_def             1 6.8349e+13 2.9885e+15 1590.1
## + max_lv_def           1 5.9818e+13 2.9970e+15 1590.2
## + max_ascencion_def    1 4.9429e+13 3.0074e+15 1590.4
## + limited              1 4.1236e+13 3.0156e+15 1590.5
## + region               4 3.5016e+14 2.7067e+15 1591.1
## + max_num_normal_atk   1 1.0638e+12 3.0558e+15 1591.2
## + max_ascencion_hp     1 1.0162e+12 3.0558e+15 1591.2
## + max_lv_hp            1 9.4834e+11 3.0559e+15 1591.2
## + base_hp              1 7.6686e+11 3.0561e+15 1591.2
## + size                 2 4.8540e+13 3.0083e+15 1592.4
## + rerun                3 1.1393e+14 2.9429e+15 1593.3
## + weapon_type          4 1.5738e+14 2.8994e+15 1594.6
## + talent_weekly       14 1.0887e+15 1.9681e+15 1595.2
## + ascension_material   8 5.4461e+14 2.5122e+15 1595.4
## + vision               6 2.8740e+14 2.7694e+15 1596.3
## + ascension            9 5.3195e+14 2.5249e+15 1597.7
## + hair_color          11 6.8574e+14 2.3711e+15 1598.5
## + ascension_boss      19 1.3176e+15 1.7393e+15 1599.0
## + talent_book_9.10    11 5.9904e+14 2.4578e+15 1600.3
## + birthmonth           8 2.6843e+14 2.7884e+15 1600.6
## + affiliation         20 1.3205e+15 1.7363e+15 1600.9
## + ascension_specialty 16 9.8382e+14 2.0730e+15 1601.8
## + eye_color           12 4.5859e+14 2.5982e+15 1605.1
## + constellation       23 1.3493e+15 1.7075e+15 1606.1
## + birthday            17 8.8420e+14 2.1726e+15 1606.1
## 
## Step:  AIC=1588.82
## revenue ~ base_atk
## 
##                       Df  Sum of Sq        RSS    AIC
## + special_3            1 1.3746e+14 2.7768e+15 1588.4
## + special_4            1 1.3746e+14 2.7768e+15 1588.4
## + special_6            1 1.3740e+14 2.7769e+15 1588.4
## + special_5            1 1.3712e+14 2.7772e+15 1588.4
## + special_2            1 1.3644e+14 2.7778e+15 1588.4
## + release_year         1 1.3441e+14 2.7799e+15 1588.5
## <none>                              2.9143e+15 1588.8
## + max_ascencion_def    1 1.1215e+14 2.8021e+15 1588.9
## + gender               1 1.0735e+14 2.8069e+15 1588.9
## + max_lv_def           1 1.0616e+14 2.8081e+15 1589.0
## - base_atk             1 1.4254e+14 3.0568e+15 1589.2
## + base_def             1 8.8663e+13 2.8256e+15 1589.3
## + limited              1 3.9105e+13 2.8752e+15 1590.1
## + max_lv_atk           1 3.4915e+13 2.8794e+15 1590.2
## + max_ascencion_atk    1 3.0954e+13 2.8833e+15 1590.3
## + region               4 3.4336e+14 2.5709e+15 1590.5
## + max_num_normal_atk   1 5.2303e+12 2.9091e+15 1590.7
## + base_hp              1 3.1104e+12 2.9112e+15 1590.8
## + max_lv_hp            1 3.2449e+11 2.9140e+15 1590.8
## + max_ascencion_hp     1 5.6481e+10 2.9142e+15 1590.8
## + size                 2 4.3600e+13 2.8707e+15 1592.1
## + rerun                3 1.5571e+14 2.7586e+15 1592.1
## + talent_weekly       14 1.0935e+15 1.8208e+15 1593.3
## + weapon_type          4 1.3751e+14 2.7768e+15 1594.4
## + ascension_material   8 5.3871e+14 2.3756e+15 1594.6
## + vision               6 2.8677e+14 2.6275e+15 1595.6
## + ascension            9 5.1631e+14 2.3980e+15 1597.1
## + hair_color          11 6.5491e+14 2.2594e+15 1598.1
## + ascension_boss      19 1.2661e+15 1.6482e+15 1598.3
## + ascension_specialty 16 1.0230e+15 1.8913e+15 1599.2
## + talent_book_9.10    11 6.0296e+14 2.3113e+15 1599.2
## + birthmonth           8 2.7898e+14 2.6353e+15 1599.8
## + affiliation         20 1.2777e+15 1.6366e+15 1600.0
## + birthday            17 9.1817e+14 1.9961e+15 1603.9
## + eye_color           12 4.7000e+14 2.4443e+15 1604.0
## + constellation       23 1.2984e+15 1.6159e+15 1605.3
## 
## Step:  AIC=1588.4
## revenue ~ base_atk + special_3
## 
##                       Df  Sum of Sq        RSS    AIC
## + release_year         1 1.3122e+14 2.6456e+15 1588.0
## + max_ascencion_def    1 1.2792e+14 2.6489e+15 1588.0
## + max_lv_def           1 1.2602e+14 2.6508e+15 1588.1
## + base_def             1 1.1142e+14 2.6654e+15 1588.4
## <none>                              2.7768e+15 1588.4
## + special_5            1 1.0802e+14 2.6688e+15 1588.4
## + special_2            1 1.0802e+14 2.6688e+15 1588.4
## + gender               1 8.8610e+13 2.6882e+15 1588.8
## - special_3            1 1.3746e+14 2.9143e+15 1588.8
## - base_atk             1 1.4185e+14 2.9187e+15 1588.9
## + region               4 3.6957e+14 2.4073e+15 1589.3
## + limited              1 4.5669e+13 2.7312e+15 1589.6
## + max_lv_atk           1 3.1711e+13 2.7451e+15 1589.8
## + max_ascencion_atk    1 2.7353e+13 2.7495e+15 1589.9
## + max_num_normal_atk   1 4.3977e+12 2.7724e+15 1590.3
## + special_6            1 2.7681e+12 2.7741e+15 1590.3
## + max_ascencion_hp     1 2.0185e+12 2.7748e+15 1590.4
## + max_lv_hp            1 7.7538e+11 2.7761e+15 1590.4
## + base_hp              1 8.7709e+08 2.7768e+15 1590.4
## + talent_weekly       14 1.1184e+15 1.6585e+15 1590.6
## + size                 2 4.1224e+13 2.7356e+15 1591.7
## + rerun                3 1.3906e+14 2.6378e+15 1591.8
## + ascension_material   8 5.2552e+14 2.2513e+15 1593.9
## + weapon_type          4 1.3279e+14 2.6440e+15 1594.0
## + ascension            9 5.8560e+14 2.1912e+15 1594.6
## + vision               6 2.8069e+14 2.4961e+15 1595.1
## + ascension_boss      19 1.2358e+15 1.5410e+15 1597.0
## + hair_color          11 6.2431e+14 2.1525e+15 1597.7
## + affiliation         20 1.2506e+15 1.5262e+15 1598.5
## + birthmonth           8 2.9083e+14 2.4860e+15 1598.9
## + ascension_specialty 16 9.7105e+14 1.8058e+15 1598.9
## + talent_book_9.10    11 5.5698e+14 2.2198e+15 1599.2
## + birthday            17 9.0958e+14 1.8672e+15 1602.6
## + constellation       23 1.2700e+15 1.5068e+15 1603.8
## + eye_color           12 4.3510e+14 2.3417e+15 1603.9
## 
## Step:  AIC=1587.98
## revenue ~ base_atk + special_3 + release_year
## 
##                       Df  Sum of Sq        RSS    AIC
## + ascension            9 8.3053e+14 1.8151e+15 1587.1
## + rerun                3 3.0594e+14 2.3397e+15 1587.8
## <none>                              2.6456e+15 1588.0
## - release_year         1 1.3122e+14 2.7768e+15 1588.4
## - special_3            1 1.3427e+14 2.7799e+15 1588.5
## + max_ascencion_def    1 7.8327e+13 2.5673e+15 1588.5
## + max_lv_def           1 7.4818e+13 2.5708e+15 1588.5
## + special_5            1 6.7646e+13 2.5780e+15 1588.7
## + special_2            1 6.7646e+13 2.5780e+15 1588.7
## - base_atk             1 1.4754e+14 2.7931e+15 1588.7
## + base_def             1 6.2795e+13 2.5828e+15 1588.8
## + limited              1 5.5312e+13 2.5903e+15 1588.9
## + gender               1 3.2174e+13 2.6134e+15 1589.4
## + max_lv_atk           1 2.7974e+13 2.6176e+15 1589.5
## + max_ascencion_atk    1 2.4003e+13 2.6216e+15 1589.5
## + max_num_normal_atk   1 5.1955e+12 2.6404e+15 1589.9
## + base_hp              1 1.0701e+12 2.6445e+15 1590.0
## + special_6            1 5.8297e+11 2.6450e+15 1590.0
## + max_ascencion_hp     1 1.5203e+11 2.6455e+15 1590.0
## + max_lv_hp            1 3.1914e+10 2.6456e+15 1590.0
## + size                 2 5.8659e+13 2.5869e+15 1590.9
## + region               4 2.4231e+14 2.4033e+15 1591.2
## + talent_weekly       14 1.0117e+15 1.6339e+15 1591.9
## + weapon_type          4 1.4287e+14 2.5027e+15 1593.2
## + ascension_material   8 4.0733e+14 2.2383e+15 1595.6
## + vision               6 1.8589e+14 2.4597e+15 1596.3
## + ascension_boss      19 1.1251e+15 1.5205e+15 1598.3
## + hair_color          11 5.4726e+14 2.0983e+15 1598.4
## + ascension_specialty 16 8.8961e+14 1.7560e+15 1599.5
## + affiliation         20 1.1241e+15 1.5215e+15 1600.3
## + birthmonth           8 1.8589e+14 2.4597e+15 1600.3
## + talent_book_9.10    11 4.3326e+14 2.2124e+15 1601.0
## + birthday            17 8.3128e+14 1.8143e+15 1603.1
## + eye_color           12 4.2539e+14 2.2202e+15 1603.2
## + constellation       22 1.1388e+15 1.5068e+15 1603.8
## 
## Step:  AIC=1587.14
## revenue ~ base_atk + special_3 + release_year + ascension
## 
##                       Df  Sum of Sq        RSS    AIC
## + rerun                3 3.6926e+14 1.4458e+15 1581.8
## + special_5            1 2.2434e+14 1.5907e+15 1582.5
## + special_2            1 2.2434e+14 1.5907e+15 1582.5
## <none>                              1.8151e+15 1587.1
## + special_6            1 4.2694e+13 1.7724e+15 1588.0
## - ascension            9 8.3053e+14 2.6456e+15 1588.0
## + gender               1 4.1452e+13 1.7736e+15 1588.0
## - special_3            1 1.2750e+14 1.9426e+15 1588.5
## + max_lv_atk           1 2.0253e+13 1.7948e+15 1588.6
## + max_ascencion_atk    1 1.8425e+13 1.7967e+15 1588.6
## + max_ascencion_def    1 1.5701e+13 1.7994e+15 1588.7
## + max_num_normal_atk   1 1.4347e+13 1.8007e+15 1588.8
## + max_lv_def           1 1.1199e+13 1.8039e+15 1588.8
## + base_def             1 5.0648e+12 1.8100e+15 1589.0
## + max_ascencion_hp     1 1.2033e+12 1.8139e+15 1589.1
## + limited              1 1.1408e+12 1.8139e+15 1589.1
## + max_lv_hp            1 4.7735e+11 1.8146e+15 1589.1
## + base_hp              1 2.3897e+09 1.8151e+15 1589.1
## - base_atk             1 1.5801e+14 1.9731e+15 1589.3
## + size                 2 2.6099e+13 1.7890e+15 1590.4
## + region               4 9.8444e+13 1.7166e+15 1592.4
## + weapon_type          4 7.3130e+13 1.7420e+15 1593.1
## - release_year         1 3.7614e+14 2.1912e+15 1594.6
## + vision               6 7.1710e+13 1.7434e+15 1597.1
## + ascension_material   7 1.1063e+14 1.7045e+15 1598.0
## + eye_color            9 2.3717e+14 1.5779e+15 1598.1
## + talent_weekly       10 2.6758e+14 1.5475e+15 1599.2
## + birthmonth           8 1.3653e+14 1.6786e+15 1599.2
## + hair_color           9 1.6902e+14 1.6461e+15 1600.3
## + talent_book_9.10    10 2.2520e+14 1.5899e+15 1600.5
## + ascension_boss      12 3.0170e+14 1.5134e+15 1602.0
## + affiliation         13 3.0825e+14 1.5068e+15 1603.8
## + ascension_specialty 13 3.0825e+14 1.5068e+15 1603.8
## + constellation       13 3.0825e+14 1.5068e+15 1603.8
## + birthday            13 3.0825e+14 1.5068e+15 1603.8
## 
## Step:  AIC=1581.77
## revenue ~ base_atk + special_3 + release_year + ascension + rerun
## 
##                       Df  Sum of Sq        RSS    AIC
## + special_2            1 1.6201e+14 1.2838e+15 1577.8
## + special_5            1 1.6201e+14 1.2838e+15 1577.8
## <none>                              1.4458e+15 1581.8
## + gender               1 2.5200e+13 1.4206e+15 1582.9
## + max_lv_atk           1 2.0905e+13 1.4249e+15 1583.0
## + max_ascencion_atk    1 1.9786e+13 1.4260e+15 1583.1
## + base_hp              1 1.5739e+13 1.4301e+15 1583.2
## + max_ascencion_def    1 1.5094e+13 1.4307e+15 1583.2
## + special_6            1 1.4566e+13 1.4313e+15 1583.3
## + limited              1 1.3297e+13 1.4325e+15 1583.3
## + max_lv_def           1 1.0404e+13 1.4354e+15 1583.4
## - special_3            1 1.1039e+14 1.5562e+15 1583.5
## + max_lv_hp            1 8.2351e+12 1.4376e+15 1583.5
## + base_def             1 4.3373e+12 1.4415e+15 1583.6
## + max_ascencion_hp     1 4.2191e+12 1.4416e+15 1583.6
## + max_num_normal_atk   1 2.0878e+12 1.4437e+15 1583.7
## + size                 2 6.4508e+12 1.4394e+15 1585.5
## + region               4 8.9651e+13 1.3562e+15 1586.6
## - base_atk             1 2.2223e+14 1.6681e+15 1586.9
## - rerun                3 3.6926e+14 1.8151e+15 1587.1
## + weapon_type          4 7.1109e+13 1.3747e+15 1587.2
## - ascension            9 8.9385e+14 2.3397e+15 1587.8
## + ascension_material   7 1.3747e+14 1.3084e+15 1590.8
## + vision               6 4.3548e+13 1.4023e+15 1592.2
## + talent_weekly       10 2.1512e+14 1.2307e+15 1593.7
## + eye_color            9 1.6287e+14 1.2830e+15 1593.8
## + talent_book_9.10    10 2.1151e+14 1.2343e+15 1593.9
## + birthmonth           8 9.2838e+13 1.3530e+15 1594.5
## + hair_color           9 1.3505e+14 1.3108e+15 1594.9
## - release_year         1 5.1739e+14 1.9632e+15 1595.1
## + ascension_boss      12 2.3550e+14 1.2103e+15 1596.9
## + affiliation         13 2.4226e+14 1.2036e+15 1598.6
## + ascension_specialty 13 2.4226e+14 1.2036e+15 1598.6
## + birthday            13 2.4226e+14 1.2036e+15 1598.6
## + constellation       13 2.4226e+14 1.2036e+15 1598.6
## 
## Step:  AIC=1577.83
## revenue ~ base_atk + special_3 + release_year + ascension + rerun + 
##     special_2
## 
##                       Df  Sum of Sq        RSS    AIC
## + talent_weekly       10 4.7042e+14 8.1339e+14 1575.0
## + ascension_material   7 3.4327e+14 9.4054e+14 1576.3
## + eye_color            9 4.0232e+14 8.8149e+14 1577.0
## <none>                              1.2838e+15 1577.8
## + special_6            1 3.8904e+13 1.2449e+15 1578.3
## + max_lv_atk           1 3.1699e+13 1.2521e+15 1578.6
## + max_ascencion_atk    1 3.0945e+13 1.2529e+15 1578.6
## + ascension_boss      12 4.7613e+14 8.0768e+14 1578.7
## + gender               1 2.4531e+13 1.2593e+15 1578.9
## + base_hp              1 1.8257e+13 1.2656e+15 1579.1
## + limited              1 1.0527e+13 1.2733e+15 1579.4
## + max_ascencion_def    1 9.7867e+12 1.2740e+15 1579.5
## + max_lv_hp            1 7.5447e+12 1.2763e+15 1579.5
## + max_lv_def           1 4.3951e+12 1.2794e+15 1579.7
## + max_ascencion_hp     1 2.7244e+12 1.2811e+15 1579.7
## + base_def             1 2.4277e+11 1.2836e+15 1579.8
## + max_num_normal_atk   1 1.3282e+11 1.2837e+15 1579.8
## + weapon_type          4 1.4079e+14 1.1430e+15 1580.0
## + region               4 1.3668e+14 1.1471e+15 1580.2
## + ascension_specialty 13 4.8292e+14 8.0089e+14 1580.2
## + affiliation         13 4.8292e+14 8.0089e+14 1580.2
## + constellation       13 4.8292e+14 8.0089e+14 1580.2
## + birthday            13 4.8292e+14 8.0089e+14 1580.2
## + size                 2 5.7109e+12 1.2781e+15 1581.6
## - special_2            1 1.6201e+14 1.4458e+15 1581.8
## - special_3            1 1.6306e+14 1.4469e+15 1581.8
## + talent_book_9.10    10 3.4212e+14 9.4169e+14 1582.3
## - rerun                3 3.0693e+14 1.5907e+15 1582.5
## - base_atk             1 2.3977e+14 1.5236e+15 1584.4
## + birthmonth           8 1.4262e+14 1.1412e+15 1587.9
## + vision               6 4.1396e+13 1.2424e+15 1588.2
## - ascension            9 1.0118e+15 2.2956e+15 1588.9
## + hair_color           9 1.3531e+14 1.1485e+15 1590.3
## - release_year         1 4.9619e+14 1.7800e+15 1592.2
## 
## Step:  AIC=1575.01
## revenue ~ base_atk + special_3 + release_year + ascension + rerun + 
##     special_2 + talent_weekly
## 
## 
## Step:  AIC=1575.01
## revenue ~ base_atk + special_3 + ascension + rerun + special_2 + 
##     talent_weekly
## 
##                       Df  Sum of Sq        RSS    AIC
## - ascension            6 1.6042e+14 9.7381e+14 1572.0
## + special_6            1 7.1910e+13 7.4148e+14 1572.4
## <none>                              8.1339e+14 1575.0
## + max_num_normal_atk   1 1.1812e+13 8.0158e+14 1576.3
## + size                 1 9.3045e+12 8.0408e+14 1576.4
## + max_lv_hp            1 7.6910e+11 8.1262e+14 1577.0
## + max_ascencion_hp     1 7.6354e+11 8.1262e+14 1577.0
## + base_hp              1 7.2938e+11 8.1266e+14 1577.0
## + max_ascencion_atk    1 6.6945e+11 8.1272e+14 1577.0
## + max_lv_atk           1 4.5542e+11 8.1293e+14 1577.0
## + max_ascencion_def    1 1.9676e+11 8.1319e+14 1577.0
## + max_lv_def           1 6.2312e+10 8.1333e+14 1577.0
## + gender               1 5.1332e+09 8.1338e+14 1577.0
## + base_def             1 1.3469e+09 8.1339e+14 1577.0
## + vision               2 5.7028e+12 8.0768e+14 1578.7
## + ascension_boss       2 5.7028e+12 8.0768e+14 1578.7
## + weapon_type          2 1.1525e+12 8.1223e+14 1578.9
## + region               3 1.2498e+13 8.0089e+14 1580.2
## + constellation        3 1.2498e+13 8.0089e+14 1580.2
## + birthday             3 1.2498e+13 8.0089e+14 1580.2
## + affiliation          3 1.2498e+13 8.0089e+14 1580.2
## + ascension_specialty  3 1.2498e+13 8.0089e+14 1580.2
## + ascension_material   3 1.2498e+13 8.0089e+14 1580.2
## + talent_book_9.10     3 1.2498e+13 8.0089e+14 1580.2
## + hair_color           3 1.2498e+13 8.0089e+14 1580.2
## + eye_color            3 1.2498e+13 8.0089e+14 1580.2
## + birthmonth           3 1.2498e+13 8.0089e+14 1580.2
## - rerun                3 2.4856e+14 1.0619e+15 1582.3
## - base_atk             1 1.6888e+14 9.8227e+14 1582.4
## - talent_weekly       11 9.6661e+14 1.7800e+15 1592.2
## - special_2            1 4.1732e+14 1.2307e+15 1593.7
## - special_3            1 4.1860e+14 1.2320e+15 1593.8
## 
## Step:  AIC=1572.01
## revenue ~ base_atk + special_3 + rerun + special_2 + talent_weekly
## 
##                       Df  Sum of Sq        RSS    AIC
## + special_6            1 7.4984e+13 8.9883e+14 1570.0
## + release_year         1 6.9037e+13 9.0477e+14 1570.3
## <none>                              9.7381e+14 1572.0
## + size                 2 6.2028e+13 9.1178e+14 1572.7
## + limited              1 1.8470e+13 9.5534e+14 1573.0
## + gender               1 1.4280e+13 9.5953e+14 1573.3
## + max_num_normal_atk   1 2.6007e+12 9.7121e+14 1573.9
## + base_def             1 8.1277e+11 9.7300e+14 1574.0
## + max_ascencion_hp     1 5.8946e+11 9.7322e+14 1574.0
## + max_lv_hp            1 5.8087e+11 9.7323e+14 1574.0
## + base_hp              1 5.2974e+11 9.7328e+14 1574.0
## + max_lv_def           1 3.9687e+11 9.7341e+14 1574.0
## + max_ascencion_atk    1 3.6126e+11 9.7345e+14 1574.0
## + max_ascencion_def    1 1.4731e+11 9.7366e+14 1574.0
## + max_lv_atk           1 8.8277e+10 9.7372e+14 1574.0
## + vision               5 1.3697e+14 8.3684e+14 1574.4
## + ascension            6 1.6042e+14 8.1339e+14 1575.0
## + region               4 7.9466e+13 8.9435e+14 1575.8
## + weapon_type          4 6.4557e+13 9.0925e+14 1576.6
## + ascension_boss       8 1.6613e+14 8.0768e+14 1578.7
## + ascension_specialty  8 1.6483e+14 8.0898e+14 1578.7
## + hair_color           8 1.6217e+14 8.1164e+14 1578.9
## - rerun                3 2.9236e+14 1.2662e+15 1579.1
## + ascension_material   8 1.4551e+14 8.2830e+14 1579.9
## + constellation        9 1.7292e+14 8.0089e+14 1580.2
## + affiliation          9 1.7292e+14 8.0089e+14 1580.2
## + eye_color            9 1.7292e+14 8.0089e+14 1580.2
## - base_atk             1 2.3222e+14 1.2060e+15 1580.7
## + birthday             8 1.2867e+14 8.4515e+14 1580.9
## + birthmonth           7 8.6406e+13 8.8741e+14 1581.4
## + talent_book_9.10     7 3.7454e+13 9.3636e+14 1584.0
## - special_2            1 3.6855e+14 1.3424e+15 1586.1
## - special_3            1 3.7014e+14 1.3439e+15 1586.1
## - talent_weekly       14 1.5556e+15 2.5294e+15 1591.7
## 
## Step:  AIC=1570
## revenue ~ base_atk + special_3 + rerun + special_2 + talent_weekly + 
##     special_6
## 
##                       Df  Sum of Sq        RSS    AIC
## + release_year         1 6.3776e+13 8.3505e+14 1568.3
## - special_3            1 8.9220e+12 9.0775e+14 1568.5
## + size                 2 8.3488e+13 8.1534e+14 1569.1
## <none>                              8.9883e+14 1570.0
## + gender               1 3.3932e+13 8.6490e+14 1570.1
## + vision               5 1.6062e+14 7.3821e+14 1570.2
## + limited              1 2.8473e+13 8.7035e+14 1570.4
## + max_num_normal_atk   1 6.2563e+12 8.9257e+14 1571.7
## + max_ascencion_atk    1 1.2052e+12 8.9762e+14 1571.9
## + base_hp              1 7.4315e+11 8.9808e+14 1572.0
## + max_lv_atk           1 6.1611e+11 8.9821e+14 1572.0
## + max_lv_hp            1 4.5318e+11 8.9837e+14 1572.0
## + max_ascencion_hp     1 2.8128e+11 8.9855e+14 1572.0
## + max_ascencion_def    1 8.4299e+10 8.9874e+14 1572.0
## + max_lv_def           1 2.3781e+10 8.9880e+14 1572.0
## + base_def             1 1.4023e+08 8.9883e+14 1572.0
## - special_6            1 7.4984e+13 9.7381e+14 1572.0
## + ascension            6 1.5735e+14 7.4148e+14 1572.4
## + region               4 6.9845e+13 8.2898e+14 1574.0
## + weapon_type          4 4.9684e+13 8.4914e+14 1575.2
## + ascension_specialty  8 1.7438e+14 7.2445e+14 1575.2
## + ascension_boss       8 1.7044e+14 7.2839e+14 1575.5
## + hair_color           8 1.6442e+14 7.3441e+14 1575.9
## + constellation        9 1.7532e+14 7.2351e+14 1577.2
## + affiliation          9 1.7532e+14 7.2351e+14 1577.2
## + eye_color            9 1.7532e+14 7.2351e+14 1577.2
## + birthmonth           7 1.0656e+14 7.9227e+14 1577.7
## + birthday             8 1.2619e+14 7.7263e+14 1578.4
## - rerun                3 3.0197e+14 1.2008e+15 1578.5
## + ascension_material   8 1.1814e+14 7.8068e+14 1579.0
## + talent_book_9.10     7 5.8302e+13 8.4053e+14 1580.7
## - base_atk             1 2.8598e+14 1.1848e+15 1581.8
## - special_2            1 4.0884e+14 1.3077e+15 1586.8
## - talent_weekly       14 1.5503e+15 2.4491e+15 1592.1
## 
## Step:  AIC=1568.32
## revenue ~ base_atk + special_3 + rerun + special_2 + talent_weekly + 
##     special_6 + release_year
## 
##                       Df  Sum of Sq        RSS    AIC
## - special_3            1 7.6961e+12 8.4275e+14 1566.8
## + size                 2 7.7196e+13 7.5786e+14 1567.5
## <none>                              8.3505e+14 1568.3
## + limited              1 2.5106e+13 8.0995e+14 1568.8
## + max_num_normal_atk   1 1.6321e+13 8.1873e+14 1569.3
## - release_year         1 6.3776e+13 8.9883e+14 1570.0
## + gender               1 1.7315e+12 8.3332e+14 1570.2
## + max_ascencion_atk    1 1.4393e+12 8.3361e+14 1570.2
## + max_lv_atk           1 9.4549e+11 8.3411e+14 1570.3
## + base_def             1 7.5946e+10 8.3498e+14 1570.3
## + max_ascencion_hp     1 2.6498e+10 8.3503e+14 1570.3
## + max_ascencion_def    1 1.7861e+10 8.3503e+14 1570.3
## + max_lv_hp            1 8.6734e+09 8.3504e+14 1570.3
## + max_lv_def           1 2.2873e+09 8.3505e+14 1570.3
## + base_hp              1 1.9024e+08 8.3505e+14 1570.3
## - special_6            1 6.9722e+13 9.0477e+14 1570.3
## + vision               5 1.0190e+14 7.3315e+14 1571.8
## + ascension            5 9.3575e+13 7.4148e+14 1572.4
## + weapon_type          4 4.7797e+13 7.8726e+14 1573.4
## + region               4 3.1986e+13 8.0307e+14 1574.4
## + ascension_specialty  7 1.1060e+14 7.2445e+14 1575.2
## + ascension_boss       7 1.0666e+14 7.2839e+14 1575.5
## + birthmonth           7 9.7357e+13 7.3770e+14 1576.1
## + talent_book_9.10     7 8.8347e+13 7.4671e+14 1576.7
## + birthday             8 1.1154e+14 7.2351e+14 1577.2
## + eye_color            8 1.1154e+14 7.2351e+14 1577.2
## + hair_color           8 1.1154e+14 7.2351e+14 1577.2
## + constellation        8 1.1154e+14 7.2351e+14 1577.2
## + affiliation          8 1.1154e+14 7.2351e+14 1577.2
## + ascension_material   7 5.4368e+13 7.8068e+14 1579.0
## - rerun                3 3.4896e+14 1.1840e+15 1579.8
## - base_atk             1 2.5903e+14 1.0941e+15 1579.8
## - special_2            1 3.9143e+14 1.2265e+15 1585.5
## - talent_weekly       14 1.3600e+15 2.1950e+15 1588.7
## 
## Step:  AIC=1566.78
## revenue ~ base_atk + rerun + special_2 + talent_weekly + special_6 + 
##     release_year
## 
##                       Df  Sum of Sq        RSS    AIC
## + size                 2 7.3299e+13 7.6945e+14 1566.2
## <none>                              8.4275e+14 1566.8
## + limited              1 2.3195e+13 8.1955e+14 1567.4
## + max_num_normal_atk   1 1.4920e+13 8.2783e+14 1567.9
## + special_3            1 7.6961e+12 8.3505e+14 1568.3
## + special_4            1 7.6961e+12 8.3505e+14 1568.3
## + special_5            1 7.6961e+12 8.3505e+14 1568.3
## - release_year         1 6.5001e+13 9.0775e+14 1568.5
## + max_ascencion_atk    1 1.0565e+12 8.4169e+14 1568.7
## + max_lv_atk           1 6.3469e+11 8.4211e+14 1568.8
## + base_def             1 4.5870e+11 8.4229e+14 1568.8
## + max_ascencion_hp     1 2.8846e+11 8.4246e+14 1568.8
## + max_lv_hp            1 2.6308e+11 8.4249e+14 1568.8
## + base_hp              1 2.1083e+11 8.4254e+14 1568.8
## + max_lv_def           1 1.7028e+11 8.4258e+14 1568.8
## + gender               1 8.8039e+10 8.4266e+14 1568.8
## + max_ascencion_def    1 3.5576e+10 8.4271e+14 1568.8
## + vision               5 9.6976e+13 7.4577e+14 1570.7
## + ascension            5 9.4874e+13 7.4787e+14 1570.8
## + weapon_type          4 4.6265e+13 7.9648e+14 1572.0
## + region               4 3.1578e+13 8.1117e+14 1572.9
## + ascension_specialty  7 1.0843e+14 7.3432e+14 1573.9
## + ascension_boss       7 1.0323e+14 7.3952e+14 1574.2
## + birthmonth           7 8.9033e+13 7.5372e+14 1575.2
## + constellation        8 1.0876e+14 7.3398e+14 1575.9
## + affiliation          8 1.0876e+14 7.3398e+14 1575.9
## + hair_color           8 1.0876e+14 7.3398e+14 1575.9
## + eye_color            8 1.0876e+14 7.3398e+14 1575.9
## + birthday             8 1.0876e+14 7.3398e+14 1575.9
## + talent_book_9.10     7 7.1828e+13 7.7092e+14 1576.3
## + ascension_material   7 6.0611e+13 7.8214e+14 1577.0
## - base_atk             1 2.5229e+14 1.0950e+15 1577.9
## - rerun                3 3.4465e+14 1.1874e+15 1577.9
## - special_2            1 4.1920e+14 1.2619e+15 1585.0
## - special_6            1 4.2030e+14 1.2630e+15 1585.0
## - talent_weekly       14 1.4098e+15 2.2525e+15 1587.9
## 
## Step:  AIC=1566.23
## revenue ~ base_atk + rerun + special_2 + talent_weekly + special_6 + 
##     release_year + size
## 
##                       Df  Sum of Sq        RSS    AIC
## <none>                              7.6945e+14 1566.2
## - size                 2 7.3299e+13 8.4275e+14 1566.8
## + special_3            1 1.1593e+13 7.5786e+14 1567.5
## + special_4            1 1.1593e+13 7.5786e+14 1567.5
## + special_5            1 1.1593e+13 7.5786e+14 1567.5
## + max_num_normal_atk   1 5.7757e+12 7.6367e+14 1567.9
## - release_year         1 5.9112e+13 8.2856e+14 1567.9
## + max_ascencion_atk    1 2.4853e+12 7.6696e+14 1568.1
## + max_lv_atk           1 2.1533e+12 7.6730e+14 1568.1
## + limited              1 1.6561e+12 7.6779e+14 1568.1
## + base_def             1 1.6547e+12 7.6779e+14 1568.1
## + base_hp              1 1.3104e+12 7.6814e+14 1568.2
## + max_lv_hp            1 1.1322e+12 7.6832e+14 1568.2
## + max_ascencion_hp     1 9.6904e+11 7.6848e+14 1568.2
## + max_lv_def           1 7.6648e+11 7.6868e+14 1568.2
## + max_ascencion_def    1 2.9267e+11 7.6916e+14 1568.2
## + gender               1 1.4268e+09 7.6945e+14 1568.2
## + region               3 2.4955e+13 7.4449e+14 1570.6
## + ascension            4 2.5412e+13 7.4404e+14 1572.5
## + weapon_type          4 7.2654e+12 7.6218e+14 1573.8
## + ascension_specialty  5 3.5133e+13 7.3432e+14 1573.9
## + vision               5 2.7694e+13 7.4175e+14 1574.4
## - rerun                3 2.5586e+14 1.0253e+15 1574.6
## + affiliation          6 3.5465e+13 7.3398e+14 1575.9
## + ascension_boss       6 3.5465e+13 7.3398e+14 1575.9
## + constellation        6 3.5465e+13 7.3398e+14 1575.9
## + birthday             6 3.5465e+13 7.3398e+14 1575.9
## + ascension_material   6 3.5465e+13 7.3398e+14 1575.9
## + talent_book_9.10     6 3.5465e+13 7.3398e+14 1575.9
## + hair_color           6 3.5465e+13 7.3398e+14 1575.9
## + eye_color            6 3.5465e+13 7.3398e+14 1575.9
## + birthmonth           6 3.5465e+13 7.3398e+14 1575.9
## - base_atk             1 2.3071e+14 1.0002e+15 1577.3
## - special_2            1 4.7902e+14 1.2485e+15 1588.4
## - special_6            1 4.8019e+14 1.2496e+15 1588.5
## - talent_weekly       14 1.3638e+15 2.1333e+15 1589.2

summary(hybridStepwise)

## 
## Call:
## lm(formula = revenue ~ base_atk + rerun + special_2 + talent_weekly + 
##     special_6 + release_year + size, data = rev1)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -9233981 -2672323  -778721  1387224 13140709 
## 
## Coefficients:
##                                             Estimate Std. Error t value
## (Intercept)                               -1.029e+10  7.287e+09  -1.412
## base_atk                                  -2.471e+06  8.849e+05  -2.792
## rerunb                                     4.020e+06  2.066e+06   1.946
## rerunc                                     6.876e+06  2.442e+06   2.816
## rerund                                     2.010e+06  4.498e+06   0.447
## special_2                                  1.289e+09  3.205e+08   4.023
## talent_weeklyBloodjade Branch              1.943e+07  6.339e+06   3.066
## talent_weeklyDragon Lord's Crown           2.440e+06  4.758e+06   0.513
## talent_weeklyGilded Scale                  7.952e+06  5.825e+06   1.365
## talent_weeklyHellfire Butterfly            3.148e+06  5.171e+06   0.609
## talent_weeklyMolten Moment                 2.086e+07  5.443e+06   3.833
## talent_weeklyMudra of the Malefic General  7.411e+06  6.783e+06   1.093
## talent_weeklyPuppet Strings                2.098e+06  1.031e+07   0.203
## talent_weeklyRing of Boreas                3.911e+06  7.996e+06   0.489
## talent_weeklyShadow of the Warrior         1.095e+06  5.040e+06   0.217
## talent_weeklyShard of a Foul Legacy        1.292e+06  5.107e+06   0.253
## talent_weeklyTail of Boreas                1.112e+07  6.422e+06   1.731
## talent_weeklyTears of the Calamitous God  -1.212e+07  8.235e+06  -1.472
## talent_weeklyThe Meaning of Aeons         -1.088e+06  6.601e+06  -0.165
## talent_weeklyTusk of Monoceros Caeli       6.323e+06  5.741e+06   1.101
## special_6                                 -1.291e+09  3.205e+08  -4.028
## release_year                               5.096e+06  3.605e+06   1.413
## sizeShort                                  9.957e+06  6.650e+06   1.497
## sizeTall                                  -1.112e+06  2.167e+06  -0.513
##                                           Pr(>|t|)    
## (Intercept)                               0.169905    
## base_atk                                  0.009689 ** 
## rerunb                                    0.062518 .  
## rerunc                                    0.009159 ** 
## rerund                                    0.658731    
## special_2                                 0.000440 ***
## talent_weeklyBloodjade Branch             0.005013 ** 
## talent_weeklyDragon Lord's Crown          0.612389    
## talent_weeklyGilded Scale                 0.183935    
## talent_weeklyHellfire Butterfly           0.547903    
## talent_weeklyMolten Moment                0.000722 ***
## talent_weeklyMudra of the Malefic General 0.284582    
## talent_weeklyPuppet Strings               0.840417    
## talent_weeklyRing of Boreas               0.628891    
## talent_weeklyShadow of the Warrior        0.829748    
## talent_weeklyShard of a Foul Legacy       0.802290    
## talent_weeklyTail of Boreas               0.095300 .  
## talent_weeklyTears of the Calamitous God  0.153146    
## talent_weeklyThe Meaning of Aeons         0.870372    
## talent_weeklyTusk of Monoceros Caeli      0.280847    
## special_6                                 0.000434 ***
## release_year                              0.169427    
## sizeShort                                 0.146349    
## sizeTall                                  0.612077    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5440000 on 26 degrees of freedom
## Multiple R-squared:  0.7483, Adjusted R-squared:  0.5256 
## F-statistic:  3.36 on 23 and 26 DF,  p-value: 0.001737

To understand what character features correlate with revenue generation, we plan to use the following three models and compare the performance of different models through metrics such as R-squared, RMSE (Root Mean Squared Error) to determine which model best captures the patterns in our data set.

Multiple Linear Regression (MLR)

Multiple linear regression assumes a linear relationship between the independent variables (character features) and the dependent variable (revenue). This approach is particularly effective as an initial strategy to investigate how different character features in our data may influence revenue. MLR is versatile, accommodating both continuous and categorical data, which enables a comprehensive evaluation of how diverse factors jointly affect revenue. Additionally, MLR can control for various confounding variables, allowing us to isolate the effect of individual character features on revenue.

#Method 1: linear regression: combining stepwise selection
lm_model = lm(revenue~base_atk + rerun + special_2 + talent_weekly + special_6 + 
                release_year + size, data = rev1)

Generalized Additive Model (GAM)

GAMs are an extension of linear models that allow for more flexible, non-linear relationships between the features and revenue without having to specify the form of the relationship a priori. If there’s reason to believe the relationship between character features and revenue isn’t strictly linear, GAMs can model these curves without needing to transform the variables explicitly.

#Method 2: nonlinear regression-gam
gam_model <- gam(revenue~s(base_atk) + rerun + s(special_2, k = 8) + talent_weekly + 
                   s(special_6, k = 8) + release_year+ size, method = 'REML', data = rev1)

Decision Tree Model

Decision trees do not assume any specific distribution for the variables, making them suitable for complex datasets with non-linear relationships that aren’t easily captured by traditional regression models. They can naturally model interactions between different character features without explicitly defining them in the model. The tree structure of the model is relatively easy to interpret and can be visualized, which is helpful for communicating results to stakeholders who may not have a technical background.

#Method 3: regression tree
rev2 <- rev %>% 
  select(-id, -character_name)
tree1 = rpart(revenue~.,data = rev2, method = 'anova')

D. Time Series - Weapons Event Revenue Analysis

The analytical techniques used ranged from a simple average model to ARIMA models to forecast upcoming events in 2024. Below is an analysis of each model used and a graph comparing to the test results.

The team plans to using a combination of the best 4 models to come up with a range of revenue results that can be expected. Below is the analysis of each model used and the conclusions found at the bottom of this section.

### SPLIT DATA
train = window(ts_data,end=c(2023,08))
test = window(ts_data, start=c(2023,09))
length(test)

## [1] 12

Average Model

average_model = meanf(train,h = 12)
average_model

##          Point Forecast    Lo 80    Hi 80     Lo 95    Hi 95
## 2023.471       96506.79 -3074.66 196088.2 -57890.23 250903.8
## 2023.529       96506.79 -3074.66 196088.2 -57890.23 250903.8
## 2023.588       96506.79 -3074.66 196088.2 -57890.23 250903.8
## 2023.647       96506.79 -3074.66 196088.2 -57890.23 250903.8
## 2023.706       96506.79 -3074.66 196088.2 -57890.23 250903.8
## 2023.765       96506.79 -3074.66 196088.2 -57890.23 250903.8
## 2023.824       96506.79 -3074.66 196088.2 -57890.23 250903.8
## 2023.882       96506.79 -3074.66 196088.2 -57890.23 250903.8
## 2023.941       96506.79 -3074.66 196088.2 -57890.23 250903.8
## 2024.000       96506.79 -3074.66 196088.2 -57890.23 250903.8
## 2024.059       96506.79 -3074.66 196088.2 -57890.23 250903.8
## 2024.118       96506.79 -3074.66 196088.2 -57890.23 250903.8

accuracy(average_model,x = test)

##                         ME     RMSE      MAE       MPE     MAPE      MASE
## Training set -6.583009e-12 74652.43 52965.43 -165.5586 191.8922 0.7245982
## Test set     -3.102337e+04 62723.79 55057.61 -179.9899 193.5421 0.7532204
##                    ACF1 Theil's U
## Training set  0.2364299        NA
## Test set     -0.2997656 0.8938043

autoplot(train)+
  autolayer(average_model,PI = F,size=1.1,series = 'Average Model')+
  autolayer(test, color ='gray')

Naive Models

naive_model = naive(train,h=12)
naive_model

##          Point Forecast     Lo 80    Hi 80     Lo 95    Hi 95
## 2023.471          29350  -88396.3 147096.3 -150727.4 209427.4
## 2023.529          29350 -137168.4 195868.4 -225317.9 284017.9
## 2023.588          29350 -174592.6 233292.6 -282553.2 341253.2
## 2023.647          29350 -206142.6 264842.6 -330804.9 389504.9
## 2023.706          29350 -233938.7 292638.7 -373315.4 432015.4
## 2023.765          29350 -259068.4 317768.4 -411747.8 470447.8
## 2023.824          29350 -282177.4 340877.4 -447090.1 505790.1
## 2023.882          29350 -303686.8 362386.8 -479985.9 538685.9
## 2023.941          29350 -323888.9 382588.9 -510882.3 569582.3
## 2024.000          29350 -342996.5 401696.5 -540104.8 598804.8
## 2024.059          29350 -361170.3 419870.3 -567899.3 626599.3
## 2024.118          29350 -378535.1 437235.1 -594456.5 653156.5

accuracy(naive_model,x = test)

##                      ME     RMSE      MAE       MPE     MAPE      MASE
## Training set   378.7561 91877.93 63761.15 -36.83240 84.19026 0.8722899
## Test set     36133.4167 65402.21 42600.42  14.84844 57.08111 0.5827987
##                    ACF1 Theil's U
## Training set -0.5098313        NA
## Test set     -0.2997656 0.9629082

### SEASONAL NAIVE MODEL
seasonal_naive_model = snaive(train,h=12)
seasonal_naive_model

##          Point Forecast      Lo 80    Hi 80      Lo 95    Hi 95
## 2023.471          49222 -81711.617 180155.6 -151023.69 249467.7
## 2023.529          35346 -95587.617 166279.6 -164899.69 235591.7
## 2023.588         100388 -30545.617 231321.6  -99857.69 300633.7
## 2023.647         132595   1661.383 263528.6  -67650.69 332840.7
## 2023.706         156895  25961.383 287828.6  -43350.69 357140.7
## 2023.765          66253 -64680.617 197186.6 -133992.69 266498.7
## 2023.824         105277 -25656.617 236210.6  -94968.69 305522.7
## 2023.882         142197  11263.383 273130.6  -58048.69 342442.7
## 2023.941          95714 -35219.617 226647.6 -104531.69 295959.7
## 2024.000         245032 114098.383 375965.6   44786.31 445277.7
## 2024.059          64279 -66654.617 195212.6 -135966.69 264524.7
## 2024.118         125472  -5461.617 256405.6  -74773.69 325717.7

accuracy(seasonal_naive_model,x = test)

##                     ME      RMSE      MAE        MPE      MAPE     MASE
## Training set   1305.64 102168.04 73096.28  -46.06752  98.56889 1.000000
## Test set     -44405.75  91243.43 77549.42 -213.16628 237.92131 1.060922
##                    ACF1 Theil's U
## Training set  0.3903477        NA
## Test set     -0.2727432  1.074854

autoplot(train)+
  autolayer(average_model,PI = F,size=1.1,series = 'Average Model')+
  autolayer(naive_model,PI=F,size=1.1, series='Naive Model')+
  autolayer(seasonal_naive_model,PI=F,size=1.1,series='Seasonal Naive Model')+
  autolayer(test, color ='gray')

Drift Model

drift_model = rwf(train,h=12,drift = T)
accuracy(drift_model,x = test)

##                         ME     RMSE      MAE        MPE     MAPE      MASE
## Training set -6.033721e-12 91877.14 63751.91 -37.833207 84.65713 0.8721635
## Test set      3.367150e+04 64479.64 41962.49   6.263651 60.04691 0.5740715
##                    ACF1 Theil's U
## Training set -0.5098313        NA
## Test set     -0.2790518 0.9572607

autoplot(train)+
  autolayer(seasonal_naive_model,PI=F,size=1.1,series='Seasonal Naive Model')+
  autolayer(drift_model,PI=F,size=1.1,series='Drift Model')+
  autolayer(test, color = 'gray')

Simple Exponential Smoothing

ses_model = ses(train,h = 12)
accuracy(ses_model,x = test)

##                    ME     RMSE      MAE       MPE      MAPE      MASE
## Training set 2841.213 72934.74 49651.80 -44.22614  74.85748 0.6792657
## Test set     6798.918 54936.78 42185.25 -70.25814 104.45827 0.5771190
##                    ACF1 Theil's U
## Training set -0.0446480        NA
## Test set     -0.2997656 0.8529142

autoplot(train)+
  autolayer(ses_model,series = "Simple Exponential Smoothing",PI = F, size=1.1)+
  autolayer(test, color = 'gray')

Holt Models

holt_model = holt(train,h=12)
accuracy(holt_model,x = test)

##                     ME     RMSE      MAE       MPE      MAPE      MASE
## Training set -14425.07 74977.13 57864.79 -69.31551 100.86112 0.7916242
## Test set      49276.33 70920.61 53195.05  73.96842  90.32874 0.7277395
##                     ACF1 Theil's U
## Training set -0.07148315        NA
## Test set     -0.49401266  1.007608

### HOLT DAMPENED MODEL
holt_damped_model = holt(train,h=12,damped = T)
accuracy(holt_damped_model,x=test)

##                     ME     RMSE      MAE        MPE      MAPE      MASE
## Training set -3924.720 70965.60 49773.87  -46.30344  82.58725 0.6809358
## Test set     -6509.459 54982.96 46690.30 -109.13397 136.02768 0.6387506
##                     ACF1 Theil's U
## Training set -0.01107696        NA
## Test set     -0.29592843 0.8454521

holt_damped_final_model = holt(ts_data,h=17,damped = T)

### HOLTS WINTER ADDITIVE
hw_additive = hw(train,h=12,seasonal = 'additive', damped=T)
accuracy(hw_additive,x = test)

##                       ME      RMSE      MAE       MPE     MAPE      MASE
## Training set   -716.6311  71600.62 47962.84  -29.1654  96.3281 0.6561598
## Test set     -68266.3279 102511.15 76594.13 -216.1654 220.3215 1.0478527
##                     ACF1 Theil's U
## Training set -0.04378591        NA
## Test set     -0.66747231 0.6294028

### HOLTS WINTER MULTIPLICATIVE
hw_multiplicative = hw(train,h=12,seasonal = 'multiplicative', damped=T)
accuracy(hw_multiplicative,x = test)

##                     ME      RMSE      MAE        MPE     MAPE      MASE
## Training set   3823.10  76849.39 48078.69  -72.70706 112.8640 0.6577447
## Test set     -63869.47 110079.49 81190.57 -217.44908 227.6671 1.1107346
##                    ACF1 Theil's U
## Training set  0.2745076        NA
## Test set     -0.6980408 0.6937347

autoplot(train)+
  autolayer(holt_model,series="Holt's Method",PI=F,size=1.1)+
  autolayer(holt_damped_model,series="Holt's Method with Damping",PI=F,size=1.1)+
  autolayer(hw_additive,series="Holt Winter's Method - Additive",PI=F)+
  autolayer(hw_additive,series="Holt Winter's Method - Multiplicative",PI=F)+
  autolayer(test, color = 'gray')

ETS Models

ets_aaa = ets(train,model = 'AAA')
checkresiduals(ets_aaa)

## 
##  Ljung-Box test
## 
## data:  Residuals from ETS(A,A,A)
## Q* = 5.2772, df = 8, p-value = 0.7276
## 
## Model df: 0.   Total lags used: 8

ets_aaa_forecast = forecast(ets_aaa,h=12)
ets_aaa_forecast

##          Point Forecast       Lo 80    Hi 80      Lo 95    Hi 95
## 2023.471       59516.44  -70248.880 189281.8 -138942.49 257975.4
## 2023.529      119018.78  -21735.175 259772.7  -96245.82 334283.4
## 2023.588      137763.03  -13186.400 288712.5  -93094.20 368620.3
## 2023.647      151916.51   -8586.443 312419.5  -93551.58 397384.6
## 2023.706      299473.53  129950.422 468996.6   40210.31 558736.7
## 2023.765      143475.48  -34615.462 321566.4 -128891.11 415842.1
## 2023.824      159943.93  -26324.973 346212.8 -124929.77 444817.6
## 2023.882      156839.04  -37267.217 350945.3 -140020.86 453698.9
## 2023.941      112342.03  -89300.702 313984.8 -196043.92 420728.0
## 2024.000      185880.72  -23030.167 394791.6 -133620.91 505382.4
## 2024.059       34190.19 -181747.643 250128.0 -296058.23 364438.6
## 2024.118       70109.92 -152636.474 292856.3 -270551.29 410771.1

accuracy(ets_aaa_forecast,x = test)

##                       ME     RMSE      MAE        MPE     MAPE      MASE
## Training set   -795.0516  71599.1 48013.12  -28.86413  96.6028 0.6568476
## Test set     -70389.0494 103944.3 78465.63 -223.43965 227.4704 1.0734559
##                     ACF1 Theil's U
## Training set -0.04481467        NA
## Test set     -0.66425556 0.6535664

### ETS AUTO MODEL
ets_auto = ets(train)
summary(ets_auto)

## ETS(M,A,N) 
## 
## Call:
##  ets(y = train) 
## 
##   Smoothing parameters:
##     alpha = 0.2696 
##     beta  = 0.0277 
## 
##   Initial states:
##     l = -34502.1219 
##     b = 15248.3664 
## 
##   sigma:  0.689
## 
##      AIC     AICc      BIC 
## 1095.022 1096.689 1103.710 
## 
## Training set error measures:
##                     ME     RMSE      MAE       MPE     MAPE      MASE
## Training set -17263.82 75262.57 58453.89 -70.49975 101.2485 0.7996835
##                     ACF1
## Training set -0.03553015

ets_auto_forecast = forecast(ets_auto, h=12)
accuracy(ets_auto_forecast,x = test)

##                     ME     RMSE      MAE       MPE      MAPE      MASE
## Training set -17263.82 75262.57 58453.89 -70.49975 101.24854 0.7996835
## Test set      40343.19 65082.33 46215.84  45.45236  69.50227 0.6322598
##                     ACF1 Theil's U
## Training set -0.03553015        NA
## Test set     -0.48534471 0.9346768

autoplot(train)+
  autolayer(ets_auto_forecast,series="ETS - MAM (auto)",PI=F)+
  autolayer(ets_aaa_forecast,series="ETS - AAA",PI=F)+
  autolayer(test, color = 'gray')

ARIMA Model

kpss.test(ts_data)

## Warning in kpss.test(ts_data): p-value greater than printed p-value

## 
##  KPSS Test for Level Stationarity
## 
## data:  ts_data
## KPSS Level = 0.18545, Truncation lag parameter = 3, p-value = 0.1

model_auto = auto.arima(y = train,d = 1,D = 1,stepwise = F,approximation = F)
model_auto

## Series: train 
## ARIMA(0,1,1)(0,1,0)[17] 
## 
## Coefficients:
##           ma1
##       -0.5812
## s.e.   0.1816
## 
## sigma^2 = 9.428e+09:  log likelihood = -309.35
## AIC=622.71   AICc=623.28   BIC=625.06

arima_forecast = forecast(model_auto, h = 12)
autoplot(train)+
  autolayer(ets_auto_forecast,series="ETS - MAM (auto)",PI=F)+
  autolayer(arima_forecast,series="ARIMA (auto)",PI=F)+
  autolayer(test, color = 'grey')

Key Findings and Discussion

A. Text Mining - Sentiment Analysis

Game Reviews

#Binary Sentiment Model Visualization 
total_sentiments <- 7005 + 4792

genshin_reviews_bin %>%
  count() %>%
  mutate(percentage = n / total_sentiments * 100) %>%
  ggplot(aes(x = percentage, y = sentiment, fill = sentiment)) +
  geom_col() +
  geom_text(aes(label = paste0(round(percentage, 1), "%")), hjust = -0.5) +
  theme_wsj() +
  guides(fill = FALSE) +
  labs(x = "Percentage", 
       y = "Sentiment",
       title = "Binary Sentiment Results") +
  scale_x_continuous(limits = c(0, 100))

## Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
## of ggplot2 3.3.4.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

The sentiment analysis uses different lexicons to provide valuable insights into user perceptions of the game. The binary analysis reveals a higher proportion of negative reviews compared to positive ones, with 59.4% (7005) negative reviews and 40.6% (4792) positive reviews. This result suggests that there is a predominance of negative sentiment among the users who posted tweets with the #boycottgenshin hashtag.

#NRC Emotion Sentiment Model Visualization
total_nrc <- genshin_reviews_nrc_emotion %>%
  summarise(total = sum(n))

genshin_reviews_nrc_emotion %>%
  mutate(percentage = n / total_nrc$total * 100) %>%
  ggplot(aes(x = reorder(sentiment, percentage), y = percentage, fill = sentiment)) +
  geom_col() +
  geom_text(aes(label = paste0(round(percentage, 1), "%")), vjust = -0.2) +
  guides(fill = FALSE) +
  coord_flip() +
  theme_wsj() +
  labs(x = "Sentiment", 
       y = "Percentage of Total NRC",
       title = "NRC Emotion Sentiment Results") +
  scale_y_continuous(limits = c(0, 30))

However, the NRC emotion analysis paints a more nuanced picture. It shows that while “negative” (17.6%) is one of the top emotions expressed, “positive” (19%) is actually the most prevalent emotion. Other notable emotions include “trust” (11.1%), “anticipation” (9.8%), and “sadness” (8.5%). This mixed bag of emotions suggests that users have varied feelings towards Genshin Impact, with a slight inclination towards positivity.

#Show the AFINN summarized results 
genshin_reviews_afinn %>% 
  summarize(min=min(reviewSentiment),
            max=max(reviewSentiment),
            median=median(reviewSentiment),
            mean=mean(reviewSentiment))

## # A tibble: 1 × 4
##     min   max median    mean
##   <dbl> <dbl>  <dbl>   <dbl>
## 1    -3     4      0 0.00271

#AFINN Sentiment Model Visualization
genshin_reviews_afinn %>% 
  ggplot(aes(x=reviewSentiment,fill=reviewSentiment>0))+
  geom_histogram(binwidth = 0.1)+
  scale_x_continuous(breaks=seq(-5,5,1))+
  scale_fill_manual(values=c('tomato','seagreen'))+
  guides(fill=F)+
  labs(title = "AFINN Sentiment Results") +
  theme_wsj()

The AFINN analysis further supports the presence of both negative and positive sentiments. The result indicates a wide range of scores from -3 to 4, with a median of 0 and a mean of 0.00279. The graph below shows the existence of a significant amount of neutral comments, defined as ranging from -1 to 1. In addition, the notable peaks in the negative range (-2) and the positive range (2) highlight the existence of strong opinions on both ends of the spectrum and demonstrate that the reviews are significantly polarized.

#show the summarized results 
genshin_reviews_Jockers %>% 
  summarize(min=min(reviewSentiment),
            max=max(reviewSentiment),
            median=median(reviewSentiment),
            mean=mean(reviewSentiment))

## # A tibble: 1 × 4
##     min   max median   mean
##   <dbl> <dbl>  <dbl>  <dbl>
## 1    -1     1 0.0333 0.0302

#Jockers Sentiment Model Visualization
genshin_reviews_Jockers %>% 
  ggplot(aes(x=reviewSentiment,fill=reviewSentiment>0))+
  geom_histogram(binwidth = 0.02)+
  scale_x_continuous(breaks=seq(-1,1,0.2))+
  scale_fill_manual(values=c('tomato','seagreen'))+
  guides(fill=F)+
  labs(title = "Jockers Sentiment Results") +
  theme_wsj()

Lastly, the Jockers analysis, which considers the context and parts of speech, reveals a slightly more positive overall sentiment. The score distribution, ranging from -1 to 1 with a median of 0.0333 and a mean of 0.0301, appears skewed towards the positive side. This suggests that when considering the nuances of language, the sentiment surrounding Genshin Impact leans toward positive.

Character Reviews

# binary sentiment analysis for all characters

library('tidytext');
library(tidyr); library(dplyr); library(ggplot2); library(ggthemes)
sentiment_fullcharacter<-data %>%
  unnest_tokens(word, text) %>%
  inner_join(get_sentiments("bing")) %>%
  count(character, sentiment) %>%
  spread(sentiment, n, fill = 0) %>%
  mutate(total = positive + negative,
         prop_positive = positive / total,
         prop_negative = negative / total) %>%
  arrange(desc(prop_positive))

## Joining with `by = join_by(word)`

## Warning in inner_join(., get_sentiments("bing")): Detected an unexpected many-to-many relationship between `x` and `y`.
## ℹ Row 232508 of `x` matches multiple rows in `y`.
## ℹ Row 3857 of `y` matches multiple rows in `x`.
## ℹ If a many-to-many relationship is expected, set `relationship =
##   "many-to-many"` to silence this warning.

topfull<-sentiment_fullcharacter%>%slice(1:5)


library('tidytext')
library(tidyr)
library(dplyr)
library(ggplot2)
library(ggthemes)



# Define custom colors for each character accorrding to the representative colors for each character
custom_colors <- c('mediumpurple','red4','turquoise', "khaki", "olivedrab3")

# Create ggplot 
ggplot(topfull, aes(x = reorder(character, prop_positive), y = prop_positive, fill = character)) +
  geom_bar(stat = "identity") +
  coord_flip() +
  geom_text(aes(label = scales::percent(prop_positive, accuracy = 0.1)),
            position = position_stack(vjust = 0.5), 
            color = "white", 
            size = 4) +
  labs(x = "Character", y = "Proportion of Positive Sentiment",
       title = "Top 5 Characters by Positive Sentiment Proportion - All") +
  theme_minimal() +
  scale_fill_manual(values = custom_colors)

# binary sentiment analysis for all characters

library('tidytext')
library(tidyr)
library(dplyr)
library(ggplot2)
library(ggthemes)


all_fivestardata1 <-# Filter 'data' to only include rows where the character name is in 'all_fivestardata'
sentiment_fullcharacter[sentiment_fullcharacter$character%in% all_fivestardata$`5-Star Characters`, ]


topfullfive<-all_fivestardata1%>%slice(1:5)


custom_colors <- setNames(c('orangered3','seagreen','royalblue','slateblue','limegreen'),
                          c('Nilou', 'Nahida', 'Albedo', 'Lisa', 'Tighnari'))

ggplot(topfullfive, aes(x = reorder(character, prop_positive), y = prop_positive, fill = character)) +
  geom_bar(stat = "identity") +
  coord_flip() +
  geom_text(aes(label = scales::percent(prop_positive, accuracy = 0.1)),
            position = position_stack(vjust = 0.5), 
            color = "white", 
            size = 4) +
  labs(x = "Character", y = "Proportion of Positive Sentiment",
       title = "Top 5 Characters by Positive Sentiment Proportion - 5 Star") +
  theme_minimal() +
  scale_fill_manual(values = custom_colors)

The analysis over the review of the characters mainly utilized the method of binary sentiment. In the whole list of the characters, the top 5 popular characters are Yaoyao, Navia, Chiori, Kaveh, Chevreuse. The corresponding range of the proportion of positive words in players’ reviews is 70.3% - 74.9%. In contrast, the top 5 popular characters are Nilou, Nahida, Albedo, Lisa, Tighnari in the 5-star character list with surprisingly lower figure range of 61.3% - 67.3%.

selected_fivestardata <- select(revenue_data_fivestar, five_star_characters, revenue, banner_days)

aggregated_data_fivestar <- selected_fivestardata %>%
  group_by(five_star_characters) %>%
  summarise(
    total_revenue = sum(revenue, na.rm = TRUE),
    total_banner_days = sum(banner_days, na.rm = TRUE)
  )

five_star_combine <- aggregated_data_fivestar %>%
  rename(character = five_star_characters) %>%
  inner_join(sentiment_fullcharacter, by = "character")

five_star_combine %>%
arrange(desc(prop_positive))

## # A tibble: 16 × 8
##    character total_revenue total_banner_days negative positive total
##    <chr>             <dbl>             <dbl>    <dbl>    <dbl> <dbl>
##  1 Nilou          15731680                19      119      245   364
##  2 Nahida         32101943                15      278      510   788
##  3 Yelan          25612693                22      227      403   630
##  4 Albedo         44573853                61      946     1649  2595
##  5 Cyno           19052023                18      276      473   749
##  6 Tighnari       19068372                18      146      231   377
##  7 Klee           54564739                64      952     1472  2424
##  8 Xiao           55752214                58     2117     3154  5271
##  9 Venti          89066439                85     1068     1547  2615
## 10 Yoimiya        55050353                58      566      792  1358
## 11 Eula           29645456                42     1438     1945  3383
## 12 Shenhe         16994406                21      374      502   876
## 13 Keqing          9505798                13      990     1309  2299
## 14 Zhongli        72328727                83     2289     2989  5278
## 15 Ganyu          58132056                62     1699     2163  3862
## 16 Tartaglia      28194502                62     1720     2141  3861
## # ℹ 2 more variables: prop_positive <dbl>, prop_negative <dbl>

library(ggplot2)
library(dplyr)
library(readr)

ggplot(five_star_combine, aes(x = total_revenue / total_banner_days, y = prop_positive, label = character)) +
  geom_point(alpha = 0.5) + 
  geom_smooth(method = "loess", color = "blue", se = TRUE) +
    geom_smooth(method = "lm", color = "purple", se = TRUE) + 
  # Changed from lm to loess
  geom_label(aes(label = character), hjust = 1.2, vjust = 1.2, check_overlap = TRUE, color = "red", size = 3) +  
  labs(
    title = "Average Revenue v.s. Positive Word Proportion",
    x = "Average Revenue",
    y = "Positive Word Proportion"
  ) +
  theme_minimal()

## Warning in geom_label(aes(label = character), hjust = 1.2, vjust = 1.2, :
## Ignoring unknown parameters: `check_overlap`

## `geom_smooth()` using formula = 'y ~ x'

## Warning: The following aesthetics were dropped during statistical transformation: label
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
##   the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
##   variable into a factor?

## `geom_smooth()` using formula = 'y ~ x'

## Warning: The following aesthetics were dropped during statistical transformation: label
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
##   the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
##   variable into a factor?

The ggplot graph displays the relationship between the average revenue and positive word proportion for each 5- star character (16 in total) where average revenue is calculated by total revenue divided by total number of banner days. We find that most plots are centered in the area of 55% - 65% of positive words and 550,000 - 1,000,000. The blue curve indicates that the trend of these 16 characters fluctuates near the average revenue of 1,000,000. However, considering of the limited sample size we can access to, we can infer that there is a positive relationship between average revenue and positive word proportion in general which is shown by the purple line.

B. Comment data Exploration Using Time-series Analysis

Based on the test results above and on the autoplots shown below, the top 2 models with the lowest RMSE are the Naive Model and Holt’s Model for frequency of 365, and ETS-auto for bi-weekly ts model. Though model selectionf rom ARIMA could not be done because of constraint, we could notice form the kpss and graphs that there is indeed seasonality in the dataset. Because of the limitation of some of the character’s data points(release time constraint), this result is just for reference only.

Result: daily

combined_forecast_plot <- autoplot(train, color='sienna') +
  autolayer(test, size=1.05, color='seagreen2') +
  autolayer(average_model, series = 'Average Model', PI=F) +
  autolayer(naive_model, series = 'Naive Model', PI=F) +
  autolayer(seasonal_naive_model, series = 'Seasonal Naive Model', PI=F) +
  autolayer(drift_model, series = 'Drift Model', PI=F) +
  autolayer(ses_model, series = 'SES Model', PI=F) +
  autolayer(holt_model, series = 'Holt Model', PI=F) +
  labs(color="Series") +
  theme_minimal()
combined_forecast_plot

Result: bi-weekly

biweek_forecast_plot<-autoplot(train_week, color='sienna')+
  autolayer(test_week,size=1.05,color='seagreen2')+
  autolayer(hw_additive,series = 'Holt Winter Additive',PI=F)+
  autolayer(hw_multiplicative,series = 'Holt Winter Multiplicative',PI=F)+
  autolayer(ets_auto_forecast,series="ETS - MAM (auto)",PI=F)+
  autolayer(ets_aaa_forecast,series = 'ETS AAA',PI=F)
biweek_forecast_plot

C. Character Revenue Analysis

Multiple linear regression model

When applying the multiple linear regression model, we make the assumption that there is a linear relationship between the attributes of a character and their revenue.

#Method 1: linear regression: combining stepwise selection
summary(lm_model)

## 
## Call:
## lm(formula = revenue ~ base_atk + rerun + special_2 + talent_weekly + 
##     special_6 + release_year + size, data = rev1)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -9233981 -2672323  -778721  1387224 13140709 
## 
## Coefficients:
##                                             Estimate Std. Error t value
## (Intercept)                               -1.029e+10  7.287e+09  -1.412
## base_atk                                  -2.471e+06  8.849e+05  -2.792
## rerunb                                     4.020e+06  2.066e+06   1.946
## rerunc                                     6.876e+06  2.442e+06   2.816
## rerund                                     2.010e+06  4.498e+06   0.447
## special_2                                  1.289e+09  3.205e+08   4.023
## talent_weeklyBloodjade Branch              1.943e+07  6.339e+06   3.066
## talent_weeklyDragon Lord's Crown           2.440e+06  4.758e+06   0.513
## talent_weeklyGilded Scale                  7.952e+06  5.825e+06   1.365
## talent_weeklyHellfire Butterfly            3.148e+06  5.171e+06   0.609
## talent_weeklyMolten Moment                 2.086e+07  5.443e+06   3.833
## talent_weeklyMudra of the Malefic General  7.411e+06  6.783e+06   1.093
## talent_weeklyPuppet Strings                2.098e+06  1.031e+07   0.203
## talent_weeklyRing of Boreas                3.911e+06  7.996e+06   0.489
## talent_weeklyShadow of the Warrior         1.095e+06  5.040e+06   0.217
## talent_weeklyShard of a Foul Legacy        1.292e+06  5.107e+06   0.253
## talent_weeklyTail of Boreas                1.112e+07  6.422e+06   1.731
## talent_weeklyTears of the Calamitous God  -1.212e+07  8.235e+06  -1.472
## talent_weeklyThe Meaning of Aeons         -1.088e+06  6.601e+06  -0.165
## talent_weeklyTusk of Monoceros Caeli       6.323e+06  5.741e+06   1.101
## special_6                                 -1.291e+09  3.205e+08  -4.028
## release_year                               5.096e+06  3.605e+06   1.413
## sizeShort                                  9.957e+06  6.650e+06   1.497
## sizeTall                                  -1.112e+06  2.167e+06  -0.513
##                                           Pr(>|t|)    
## (Intercept)                               0.169905    
## base_atk                                  0.009689 ** 
## rerunb                                    0.062518 .  
## rerunc                                    0.009159 ** 
## rerund                                    0.658731    
## special_2                                 0.000440 ***
## talent_weeklyBloodjade Branch             0.005013 ** 
## talent_weeklyDragon Lord's Crown          0.612389    
## talent_weeklyGilded Scale                 0.183935    
## talent_weeklyHellfire Butterfly           0.547903    
## talent_weeklyMolten Moment                0.000722 ***
## talent_weeklyMudra of the Malefic General 0.284582    
## talent_weeklyPuppet Strings               0.840417    
## talent_weeklyRing of Boreas               0.628891    
## talent_weeklyShadow of the Warrior        0.829748    
## talent_weeklyShard of a Foul Legacy       0.802290    
## talent_weeklyTail of Boreas               0.095300 .  
## talent_weeklyTears of the Calamitous God  0.153146    
## talent_weeklyThe Meaning of Aeons         0.870372    
## talent_weeklyTusk of Monoceros Caeli      0.280847    
## special_6                                 0.000434 ***
## release_year                              0.169427    
## sizeShort                                 0.146349    
## sizeTall                                  0.612077    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5440000 on 26 degrees of freedom
## Multiple R-squared:  0.7483, Adjusted R-squared:  0.5256 
## F-statistic:  3.36 on 23 and 26 DF,  p-value: 0.001737

pred_lm = predict(lm_model)
rmse_lm = sqrt(mean((pred_lm-rev1$revenue)^2)); rmse_lm

## [1] 3922880

Based on the regression analysis, we discovered that the character’s basic attack value, rerun time, special skill statistics at 2✦ and 6✦, and the required talent leveling materials obtained from weekly bosses all have a statistically significant impact on the characters’ revenue generation.

In order to provide a more concise perspective, we generated graphs illustrating the partial effect of each relevant explanatory variable.

#Plot the partial effect graph
library(effects)

## Loading required package: carData

## lattice theme set by effectsTheme()
## See ?effectsTheme for details.

plot(allEffects(lm_model)$base_atk)

plot(allEffects(lm_model)$special_2)

plot(allEffects(lm_model)$special_6)

rerun_df <- as.data.frame(allEffects(lm_model)$rerun)
rerun <- ggplot(rerun_df, aes(x = factor(rerun), y = fit)) +
  geom_point() +
  geom_errorbar(aes(ymin = lower, ymax = upper), width = 0.1) +
  theme_minimal() +
  theme(axis.text.x = element_text(vjust = 1, hjust = 1)) +
  labs(x = "rerun", y = "revenue")
rerun

effect_df <- as.data.frame(allEffects(lm_model)$talent_weekly)
talent_weekly <- ggplot(effect_df, aes(x = factor(talent_weekly), y = fit)) +
  geom_point() +
  geom_errorbar(aes(ymin = lower, ymax = upper), width = 0.1) +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1)) +
  labs(x = "talent weekly", y = "revenue")
talent_weekly

The negative impact of the basic attack value on revenue is readily apparent. The idea we have is that game designers typically provide characters with low base attack values greater potential for improvement, hence increasing players’ motivation to upgrade these characters.

Character upgrades in Genshin Impact can be attained through many means, including completing missions, battling monsters for materials, acquiring more powerful weapons from the card pool, and frequently obtaining the character to boost their star rating. This is also the main way of revenue generation in the game. Furthermore, our findings indicate that a character’s revenue is positively influenced by a greater special skill value upon reaching 2✦, but negatively impacted when the value reaches 6✦. TTis is also in line with player expenditure, as achieving a 6✦ character necessitates drawing the character from the character card pool on seven occasions (with the initial draw being 0 stars), which typically entails significant spending and a lengthy gameplay duration. Attaining a 2✦ is far less challenging compared to obtaining a 6✦. Therefore, assigning a higher value to a character’s special ability at 2✦ will serve as a strong incentive for players to invest more.

Furthermore, we learned that certain talent leveling materials, such as Bloodjade Branch and Molten Moment, which are obtained by defeating bosses, have a notable impact on revenue through a positive feedback mechanism. Therefore, we can enhance the likelihood of obtaining these materials to facilitate character upgrades.

Due to the ongoing updates in Genshin Impact, there is a potential for reruns of all characters save for the restricted ones. From the regression results, we find that the first time a character reruns (labeled b) has a positive effect on revenue at the 10% level of significance, while the second time a character reruns (labeled c) has a positive effect on generating revenue at the 1% level of significance. As a result, game designers can appropriately think about giving characters a one- or two-time of rerun to boost in-game revenue.

#Anova analysis
anova(lm_model)

## Analysis of Variance Table
## 
## Response: revenue
##               Df     Sum Sq    Mean Sq F value    Pr(>F)    
## base_atk       1 1.4254e+14 1.4254e+14  4.8165 0.0373182 *  
## rerun          3 1.5571e+14 5.1904e+13  1.7539 0.1807273    
## special_2      1 1.1984e+14 1.1984e+14  4.0493 0.0546566 .  
## talent_weekly 14 1.2948e+15 9.2485e+13  3.1251 0.0058210 ** 
## special_6      1 4.3620e+14 4.3620e+14 14.7394 0.0007101 ***
## release_year   1 6.5001e+13 6.5001e+13  2.1964 0.1503509    
## size           2 7.3299e+13 3.6649e+13  1.2384 0.3063851    
## Residuals     26 7.6945e+14 2.9594e+13                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

We also performed an ANOVA analysis of the MLR model, and based on the results above, we find that various talent leveling materials dropped from weekly bosses, different levels of the basic attack statistic, and special skill statistics at 2✦ and 6✦ have significant effects on revenue at the 5%, 0.1%, and 1% significance levels, respectively. This indicates that these character features do have a significant impact on the character’s ability to generate revenue.

Generalized Additive Model

#Method 2: nonlinear regression-gam
summary(gam_model)

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## revenue ~ s(base_atk) + rerun + s(special_2, k = 8) + talent_weekly + 
##     s(special_6, k = 8) + release_year + size
## 
## Parametric coefficients:
##                                             Estimate Std. Error t value
## (Intercept)                               -1.029e+10  7.287e+09  -1.412
## rerunb                                     4.020e+06  2.066e+06   1.946
## rerunc                                     6.876e+06  2.442e+06   2.816
## rerund                                     2.010e+06  4.498e+06   0.447
## talent_weeklyBloodjade Branch              1.943e+07  6.339e+06   3.066
## talent_weeklyDragon Lord's Crown           2.440e+06  4.758e+06   0.513
## talent_weeklyGilded Scale                  7.952e+06  5.825e+06   1.365
## talent_weeklyHellfire Butterfly            3.149e+06  5.171e+06   0.609
## talent_weeklyMolten Moment                 2.086e+07  5.443e+06   3.833
## talent_weeklyMudra of the Malefic General  7.411e+06  6.783e+06   1.093
## talent_weeklyPuppet Strings                2.097e+06  1.031e+07   0.203
## talent_weeklyRing of Boreas                3.911e+06  7.996e+06   0.489
## talent_weeklyShadow of the Warrior         1.095e+06  5.040e+06   0.217
## talent_weeklyShard of a Foul Legacy        1.292e+06  5.107e+06   0.253
## talent_weeklyTail of Boreas                1.112e+07  6.422e+06   1.731
## talent_weeklyTears of the Calamitous God  -1.212e+07  8.235e+06  -1.472
## talent_weeklyThe Meaning of Aeons         -1.088e+06  6.601e+06  -0.165
## talent_weeklyTusk of Monoceros Caeli       6.323e+06  5.741e+06   1.101
## release_year                               5.096e+06  3.605e+06   1.413
## sizeShort                                  9.957e+06  6.650e+06   1.497
## sizeTall                                  -1.112e+06  2.167e+06  -0.513
##                                           Pr(>|t|)    
## (Intercept)                               0.169901    
## rerunb                                    0.062517 .  
## rerunc                                    0.009158 ** 
## rerund                                    0.658739    
## talent_weeklyBloodjade Branch             0.005013 ** 
## talent_weeklyDragon Lord's Crown          0.612366    
## talent_weeklyGilded Scale                 0.183943    
## talent_weeklyHellfire Butterfly           0.547866    
## talent_weeklyMolten Moment                0.000722 ***
## talent_weeklyMudra of the Malefic General 0.284579    
## talent_weeklyPuppet Strings               0.840421    
## talent_weeklyRing of Boreas               0.628865    
## talent_weeklyShadow of the Warrior        0.829712    
## talent_weeklyShard of a Foul Legacy       0.802271    
## talent_weeklyTail of Boreas               0.095295 .  
## talent_weeklyTears of the Calamitous God  0.153150    
## talent_weeklyThe Meaning of Aeons         0.870375    
## talent_weeklyTusk of Monoceros Caeli      0.280832    
## release_year                              0.169424    
## sizeShort                                 0.146350    
## sizeTall                                  0.612122    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##              edf Ref.df      F  p-value    
## s(base_atk)    1      1  7.795 0.009693 ** 
## s(special_2)   1      1 16.181 0.000441 ***
## s(special_6)   1      1 16.221 0.000436 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.526   Deviance explained = 74.8%
## -REML = 450.92  Scale est. = 2.9594e+13  n = 50

pred_gam = predict(gam_model)
rmse_gam = sqrt(mean((pred_gam-rev1$revenue)^2)); rmse_gam

## [1] 3922856

Since GAM can better capture non-linear relationships between the features and revenue, we consider using this model as an extended comparison of MLR. Its regression findings are nearly identical to MLR’s, supporting the validity of the MLR conclusion mentioned above once more.

Decision tree model

#Method 3: regression tree
tree1$variable.importance

##       constellation       talent_weekly            birthday ascension_specialty 
##        1.060885e+15        7.896842e+14        7.041439e+14        5.038690e+14 
##           eye_color           ascension   max_ascencion_atk          max_lv_atk 
##        5.038690e+14        4.318877e+14        3.941862e+14        3.941862e+14 
##            base_atk          hair_color          birthmonth             base_hp 
##        3.913727e+14        1.418526e+14        1.182105e+14        1.176973e+14 
##    max_ascencion_hp           max_lv_hp  ascension_material              region 
##        8.559804e+13        8.559804e+13        7.092632e+13        7.092632e+13 
##        special_dish           special_2           special_3 
##        5.631231e+13        5.349878e+13        5.349878e+13

rpart.plot(tree1)

pred_tree = predict(tree1)
rmse_tree = sqrt(mean((pred_tree-rev2$revenue)^2)); rmse_tree

## [1] 5550443

Decision tree is a more advanced model. It is especially helpful when there is a complex relationship - for instance, one that is non-linear or involves some interaction - between character characteristics and revenue that a linear model is unable to adequately describe. The outcome is seen below. We put all the characteristics into the decision tree model and let it to choose the decision node on its own.

#Compare rmse of each model
model <- c("Multiple linear regression", "Generalized Additive Model", 
           "Decision Tree Model")
rmse <- c(rmse_lm, rmse_gam, rmse_tree)

rmse_df <- data.frame("model" = model, "rmse" = rmse)
rmse_df

##                        model    rmse
## 1 Multiple linear regression 3922880
## 2 Generalized Additive Model 3922856
## 3        Decision Tree Model 5550443

Examining the RMSE findings of these three models, we can see that the decision tree model has a high RMSE while the results of MLR and GAM differ relatively little. This is due to the fact that dealing with big, complicated datasets where interactions and non-linear correlations are predicted benefits machine learning techniques like decision trees. Using a decision tree could not give enough information to develop the structure for the current data set of 5-star characters published by Genshin Impact, depending on the quantity of data available; on the other hand, because linear regression is simpler, it might be easier to derive appropriate conclusions from less data.

D. Time Series - Weapons Event Revenue Analysis

Based on the test results from each model, the top 3 models that have the lowest RMSE are the Simple Exponential Smoothing Model, Holt’s Dampened Model, and the Average Model. However, these models do not capture trend or shifts from seasonality so the Arima model will also be used in the final forecast to capture these trends.

rbind(average_model = accuracy(object = average_model,x = test)[2,],
      naive_model = accuracy(object = naive_model,x = test)[2,],
      seasonal_naive_model = accuracy(object = seasonal_naive_model,x = test)[2,],
      drift_model = accuracy(object = drift_model,x = test)[2,],
      ses_model = accuracy(object = ses_model,x = test)[2,],
      holt_model = accuracy(object = holt_model,x = test)[2,],
      holt_damped_model = accuracy(object = holt_damped_model,x = test)[2,],
      hw_additive_model = accuracy(object = hw_additive,x = test)[2,],
      hw_multiplicative = accuracy(object = hw_multiplicative,x = test)[2,],
      ets_aaa = accuracy(ets_aaa_forecast,x = test)[2,],
      ets_auto = accuracy(ets_auto_forecast,x = test)[2,],
      arima = accuracy(arima_forecast,x= test)[2,]
)

##                              ME      RMSE      MAE         MPE      MAPE
## average_model        -31023.369  62723.79 55057.61 -179.989878 193.54212
## naive_model           36133.417  65402.21 42600.42   14.848444  57.08111
## seasonal_naive_model -44405.750  91243.43 77549.42 -213.166275 237.92131
## drift_model           33671.502  64479.64 41962.49    6.263651  60.04691
## ses_model              6798.918  54936.78 42185.25  -70.258139 104.45827
## holt_model            49276.327  70920.61 53195.05   73.968417  90.32874
## holt_damped_model     -6509.459  54982.96 46690.30 -109.133973 136.02768
## hw_additive_model    -68266.328 102511.15 76594.13 -216.165422 220.32151
## hw_multiplicative    -63869.472 110079.49 81190.57 -217.449079 227.66713
## ets_aaa              -70389.049 103944.26 78465.63 -223.439646 227.47036
## ets_auto              40343.187  65082.33 46215.84   45.452363  69.50227
## arima                 -7860.085  80095.41 63578.53 -107.138328 156.91705
##                           MASE       ACF1 Theil's U
## average_model        0.7532204 -0.2997656 0.8938043
## naive_model          0.5827987 -0.2997656 0.9629082
## seasonal_naive_model 1.0609215 -0.2727432 1.0748543
## drift_model          0.5740715 -0.2790518 0.9572607
## ses_model            0.5771190 -0.2997656 0.8529142
## holt_model           0.7277395 -0.4940127 1.0076085
## holt_damped_model    0.6387506 -0.2959284 0.8454521
## hw_additive_model    1.0478527 -0.6674723 0.6294028
## hw_multiplicative    1.1107346 -0.6980408 0.6937347
## ets_aaa              1.0734559 -0.6642556 0.6535664
## ets_auto             0.6322598 -0.4853447 0.9346768
## arima                0.8697916 -0.2727432 0.9280565

rbind(average_model = accuracy(object = average_model,x = test)[2,],
      ses_model = accuracy(object = ses_model,x = test)[2,],
      holt_damped_model = accuracy(object = holt_damped_model,x = test)[2,],
      arima = accuracy(arima_forecast,x= test)[2,]
      )

##                           ME     RMSE      MAE        MPE     MAPE      MASE
## average_model     -31023.369 62723.79 55057.61 -179.98988 193.5421 0.7532204
## ses_model           6798.918 54936.78 42185.25  -70.25814 104.4583 0.5771190
## holt_damped_model  -6509.459 54982.96 46690.30 -109.13397 136.0277 0.6387506
## arima              -7860.085 80095.41 63578.53 -107.13833 156.9171 0.8697916
##                         ACF1 Theil's U
## average_model     -0.2997656 0.8938043
## ses_model         -0.2997656 0.8529142
## holt_damped_model -0.2959284 0.8454521
## arima             -0.2727432 0.9280565

Final Forecast for 2024

average_model_final = meanf(ts_data,h = 17)
ses_model_final = ses(ts_data, h = 17)
holt_damped_model_final = holt(ts_data,h=17,damped = T)
arima_final = auto.arima(y = ts_data,d = 1,D = 1,stepwise = T,approximation = F)

arima_final_forecast = forecast(arima_final,h=17)

autoplot(ts_data, color = 'black') +
  autolayer(average_model_final,PI = F, series = 'Average Model', color = 'red')+
  autolayer(arima_final_forecast, series = 'ARIMA', PI = FALSE, color = 'blue') +
  autolayer(ses_model_final, series = 'Simple Exponential Smoothing', PI = FALSE, color = 'green') +
  autolayer(holt_damped_model_final, series = 'Holt', PI = FALSE, color = 'orange')

Future Application

library(readr)
comments_data_new_1 <- read_csv("comments_data_new.csv")

## Rows: 662 Columns: 4
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (4): user, time, text, character
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

new<- comments_data_new_1

library('tidytext');
library(tidyr); library(dplyr); library(ggplot2); library(ggthemes)
new%>%
  unnest_tokens(word, text) %>%
  inner_join(get_sentiments("bing")) %>%
  count(character, sentiment) %>%
  spread(sentiment, n, fill = 0) %>%
  mutate(total = positive + negative,
         prop_positive = positive / total,
         prop_negative = negative / total) %>%
  arrange(desc(prop_positive))

## Joining with `by = join_by(word)`

## # A tibble: 1 × 6
##   character  negative positive total prop_positive prop_negative
##   <chr>         <dbl>    <dbl> <dbl>         <dbl>         <dbl>
## 1 Arlecchino      496      555  1051         0.528         0.472

A new character, Arlecchino, was published on 24th, April, 2024. We applied sentiment analysis on the reviews of this character, and the positive word proportion is 52.8%. According to the graph of positive word proportion v.s. average revenue we generated above, we can predict the average revenue would be 500,000 which is lower than the existed characters.

df <- data.frame("base_atk" = 1.71054410, "rerun" = "a", "special_2" = 0.67404647, 
                 "talent_weekly" = "Ashen Heart", 
                 "special_6" = 0.67392712, "release_year" = 2024,
                 "size" = "Tall")
predict_new = predict(lm_model, newdata = df)

We also use the MLR model to predict the total revenue of Arlecchino after her first release. But due to the data limitation, the talent leveling material for Arlecchino is not included in our original data set. We just use one of the existing material as a reference in the prediction. Thus, we can predict that the total revenue of Arlecchino after this banner event would be 20,834,310.

Conclusion

The analysis reveals that Genshin Impact has captured significant player interest and engagement, as evidenced by the extensive volume of tweets and the broad spectrum of emotions expressed, from excitement to frustration. Despite the game’s popularity, the prevalence of negative reviews and emotions such as sadness and anger suggest that there are aspects of the game that could be improved to enhance player satisfaction. To address these issues, the company should delve deeper into the specific elements of the game causing dissatisfaction and make necessary updates. Additionally, improving communication with players and employing media advertising strategies could help increase player retention.

In terms of character-specific analysis, it appears that non 5-star characters often exceed player expectations more so than 5-star characters, both in terms of positive sentiment and revenue generation. This discrepancy likely stems from the higher expectations players place on 5-star characters, leading to greater disappointment if those expectations are not met. To balance player expectations and experiences, the game’s developers should consider adjusting the ratio of 5-star to non-5-star characters. Furthermore, enhancing the skills and abilities of 5-star characters could provide a more distinguished and satisfying experience. Offering players a trial of 5-star characters before their official release could also gather valuable feedback for further refinement.

Based on the character revenue analysis, it is recommended that the designers of Genshin Impact conduct a detailed evaluation of the basic attack values and special skill statistics at 6 ✦ to identify the underlying reasons for the negative revenue impacts and to enhance the character’s special skills at 2 ✦ accordingly. The importance of the rerun variable indicates that reintroducing characters can be an effective way to boost revenue, although this strategy needs to be fine-tuned to prevent decreasing returns with successive reruns. Additionally, the release of new characters should be leveraged as strategic opportunities to boost income by tapping into the excitement for new content among the player base. To foster player satisfaction and increase revenue growth, the process of character development should be continuously refined, guided by regular analysis of revenue trends and player feedback.

Lastly, revenue from weapon pulls is projected to decline in 2024, as many players already possess the necessary weapons. To reinvigorate interest in this area, the introduction of new weapons and the organization of special events, particularly around the New Year, could help maintain and potentially increase revenue. Regular updates and enhancements based on player feedback and revenue trends are essential for sustaining interest and satisfaction among the game’s community.

Genshin Impact: Aligning Player and Business Needs Through Data Driven Recommendations

David Nakashima, Kun Shang, Chengmin Xu, Jingwen Yi, Talia Zhuang

2024-04-26

Statement of the Research Problem

Data & Sutability

A. Text Mining - Sentiment Analysis

B. Character Revenue Analysis

C. Time Series - Weapons Event Revenue Analysis

Analysis Methods

A. Text Mining - Sentiment Analysis

Binary Sentiment Model

NRC Emotion Sentiment Model

AFINN Sentiment Model

Jockers Sentiment Model

B. Comment data Exploration Using Time-series Analysis

Data Preperation

Basic Plots

Time Series Analysis

Regular TS-simple forcasting model

Regular TS-average method

Regular TS-naive method

Regular TS-seasonal naive method

Regular TS-drift method

Regular TS-exponential smoothing models-simple exponential smoothing

Regular TS-holt’s

Regular TS-holt’s damp

Regular TS-arima (model could not be performed because of data constraints)

Regular TS- lags

C. Character Revenue Analysis

Multiple Linear Regression (MLR)

Generalized Additive Model (GAM)

Decision Tree Model

D. Time Series - Weapons Event Revenue Analysis

Average Model

Naive Models

Drift Model

Simple Exponential Smoothing

Holt Models

ETS Models

ARIMA Model

Key Findings and Discussion

A. Text Mining - Sentiment Analysis

Game Reviews

Character Reviews

B. Comment data Exploration Using Time-series Analysis

Result: daily

Result: bi-weekly

C. Character Revenue Analysis

Multiple linear regression model

Generalized Additive Model

Decision tree model

D. Time Series - Weapons Event Revenue Analysis

Final Forecast for 2024

Future Application

Conclusion